Another potential counter could be the Disarming Attack combat maneuver, or the Disarm combat option (if the DM allows it). Both just require the attacker to make a "weapon attack", not specifically a melee weapon attack. So the attacker could make a ranged attack to disarm, and if successful, use their move to close to 5', then either draw a melee weapon and use any extra attacks they may have, or pick up your dropped pole arm to prevent you from picking it up on your turn.

No, you are not unbeatable, the are many ways it doesn't work

First, there are range characters, like archers, and spellcasters who don't care about melee feats, and can "kill you lots". Many martial characters have access to Misty Step, can bamph beside you as a bonus action, and then attack you. It only works once in a turn, but if your doing a PvP thing, then this last point is less relevant, but does use up you reaction, which takes all other reactions off the table.

However, once an intelligent/experienced character sees you have a pole-arm, it is a dead give away in how to approach anyone wielding this weapon. The easiest way to attack is just declare the Disengage Action.

If you take the Disengage action, your movement doesn't provoke opportunity attacks for the rest of the turn.

and since the character no longer provokes OA's, Anyone can run up to your face, and then: cast a quickened spell cast a Bonus Action spell make a bonus action attack or any number of other Bonus Action choices A Rogue can use their Bonus Action to use Disengage, run up to your face and use their entire attack action to mess up your pretty face, and your character can't do squat about it until their next turn.

"But wait! Sentinel allows me to hit creatures who are using the Disengage action, so I still get the OA!"

Unfortunately, Sentinel doesn't work that way, it is very specific about when this special ability applies. You can only hit a disengaged character that is leaving your 5' range, it does not apply to entering (and according to Jeremy Crawford @ Sage Advice, the 5 foot specific is your reach, not your 10 foot polearm reach).

Creatures within 5 feet of you provoke opportunity attacks from you, even if they take the Disengage action, before leaving your reach.

Nor does your 10' reach apply to Sentinel, as it only applies to those within 5' (see above, and confirmed with Sage Advice). Disengage does not stipulate which way you run, nor is it negated by actions taken with the Bonus Action (again, see above). If you decide to move away, you either not attack and use the disengage yourself (no Opportunity, and now no regular attacks), or you choose to attack normally and move away, now THEY get an Opportunity Attack on you instead! The Swashbuckler Fancy Footwork completely destroys this entire combo and they can run around in front of you all day. Note that the Swashbuckler ability is just to make an attack, no "successful hit" is required to activate the ability.

During your turn, if you make a melee attack against a creature, that creature can't make opportunity attacks against you for the rest of your turn.

I appreciate that you have asked the question, because so many players think they have figured out some great "system", only to find that they didn't read the rules properly and this "unbeatable character" they thought they had, is now getting his butt handed to him repeatedly, because he doesn't do what they thought he did.

One way to mitigate could be to move to 15', then Drop to Prone and crawl to 10' provoking an OA with Disadvantage (you are more than 5' away). And then stand and move to 5'. Attack.

Orcs are especially good at this, due to Aggressive.

Obvious downside is that you may end up Prone with 0' speed left. OTOH if you are, they need to close to 5' to get rid of their Disadvantage. At which point you're good to go.

To answer your question, polearm master's second perk would activate once the enemy enters your reach (10'), and therefore a hit would stop him at that distance.

Keep in mind, however, that unless you have the Tunnel Fighter Fighting style (see below), you cannot use this more than once per round, as opportunity attacks use your reaction. You also sacrifice any other options for which you would need a reaction, which can make some feel like a one-trick pony during extended fights.

This combination is also extremely situationnal and requires a few conditions to be met. You must be able to reach the enemies (faster enemies might skirt around you or, for some, fly over/burrow under), and they must rely solely on 5' range melee attacks, which becomes void at later levels.

As for the use of Battlemaster, once again using your superiority die for this blocks other options which might be more useful or provide a more fun combat encounter. Also like your reaction, superiority die are a limited resource.

Last but not least, this requires 2 feats, and while this is not a problem for a fighter that has 7 APIs, it is not ideal for other classes who only have 5.

Here, however, are a few positive aspects of this combination:

• Tunnel Fighter (UA) removes the limit imposed by a single reaction. If you choose your positioning carefully, you can therefore stop an entire enemy party in a narrow passage, so long as those enemies are within melee range, and you don't miss an attack, of course. If you are a DM, consider this carefully before including this material in the game.
• This feat is a great opportunity for cooperative play! If you have casters with mold earth, movement-restricting spells or wall spells, use this to your advantage! Since you won't necessarily be doing mountains of damage, you can hold the front line while your allies pelt your enemies with ranged attacks while funneling your adversaries into your reach.
• Take it with the Mobile Feat. If you're hell bent on spending ASIs on feats instead of ability score upgrades, take the mobile feat, which will allow you to back off on your turn after hitting the enemy without taking an attack opportunity from it is it has 10' range as well.

Yes, it does

As you mentioned, Polearm Master lets you make an Opportunity attack as someone enters your reach; Sentinel lets you drop an enemy's speed to 0. This also applies while they're still 10' away from you, meaning that unless they have a reach weapon, they can't then make a melee attack against you.

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So, you may say to yourself:

Wow, that's stupidly good

And the answer is that it's a highly specialized combo, so it is quite good -- if you're only concerned about duels. Dueling is not the most common combat situation in D&D 5e^[1] so you're likely to run into some of the following issues, which limit the combo's usefulness in open combat:

• You only get one reaction. This limits you to locking down a single enemy at a time, so this isn't quite as useful when going up against 2 or more enemies. The more enemies you fight at once, of course, the less useful it becomes.

• They can go around you. You can penalize enemies by making use their movement like this, but you can't hold them back forever, barring favorable terrain.

• This only triggers if they enter your range so if you fail to clear your area of influence, and an enemy starts within 10' of you, they're unhindered.

• It's not guaranteed. Yeah, with the use of Precision Attack it gets up there. But, with the critical failure rules in place on Attack rolls, you're still failing to stop them about 5% of the time.

• This doesn't address ranged attacks. So, anybody with a bow or ranged spells doesn't need to get close to hit you. Of course, thanks to Sentinel, you can always do the inverse of the strategy you suggested -- close distance on spell casters and prevent them from fleeing.

[1]: At least in my games, you're more likely to run into more than one opponent at a time.

TL:DR Heck No

An example of something that would give the OP's fighter trouble (and perhaps a more ironclad one) would be going up against a War Caster Bard using Dissonant Whispers.

If the bard wins initiative, he can simply cast the spell -- without the ability to interrupt it with an opportunity attack. Now you're stuck making a Wisdom save, which the Fighter isn't so hot at.

If the bard loses initiative, it actually gets worse for the fighter -- the bard can use War Caster to cast Dissonant Whispers as a reaction to your attack, denying you the ability to disrupt it with an attack of your own. Failing that Wisdom save then makes life even tougher, because then your reaction goes up in smoke from the spell's effect, and you're now 30' away from the bard, who has his turn now available to do whatever he pleases.

No

For this to work it requires:

1. You to hit with the opportunity attack every time,

2. The opponent to have no reach or ranged options available,

3. there to be only one opponent because you only get one reaction,

4. The opponent to be an idiot.

No 1. is not going to happen, even if you have a massive bonus to hit you will eventually roll a 1.

No 2. is unlikely; most enemies have some way of doing damage at range.

No 3. Is a self-evident limitation - the first opponent sacrifices themselves to clear a path.

No 4. presupposes that the opponent has no options or will not use the options they have. A disengage action allows them to get close; a grapple stops you moving away, for example. A rogue can do this turn after turn with their Cunning Action (PHB 96); other classes have different techniques.

Note that the Sentinel ability against Disengage (PHB 192) is: "Creatures provoke opportunity attacks from you even if they take the Disengage action before leaving your reach."; it won't help with creatures 10 feet away from entering your reach or moving from 10 feet to 5 feet as they are not "leaving your reach".

Well, they could use something to make you lose your reaction. There could be two people and you only have one reaction. They could disengage the first turn and get next to you and then you would only be able to do anything if you disengaged or took an OA. You could miss. They could have range. They could have reach. They could teleport.