How do I prevent new villager trades from spawning?

I don't know much about custom villager trading, and a cursory glance over the NBT structure of villagers didn't reveal anything new to me.

As for your second point, there's a perfect technical block that should work for the newer versions: The Barrier.

Not only is it unobtainable without creative/commands, but it's icon is this:

It's itemID is barrier, so you can try

/summon Villager ~ ~ ~ {
  Offers:{Recipes:[
    {maxUses:1337,buy:{id:diamond},sell:{id:emerald}},
    {maxUses:1,buy:{id:barrier,tag:{display:{Name:No More Trades}}},sell:{id:barrier,tag:{display:{Name:No More Trades}}}}
  ]}}

Which sells renamed Barriers for renamed Barriers. You might need to use minecraft:barrier instead of just barrier, I'm not sure about that.

I'm almost one hundred percent certain that the other comment won't work. However, what will work is this:

/summon Villager ~ ~ ~ {CustomName:Billy,Profession:4,CareerLevel:6,Offers:{Recipes:[{maxUses:99999,buy:{id:"minecraft:emerald",Damage:0,Count:10},buyB:{id:"minecraft:book",Damage:0,Count:1},sell:{id:"minecraft:dye",Damage:5,Count:20}}]}}

When this command is triggered, it will summon a villager with the name Billy, who wears a white apron. He will trade you 20 purple dyes for 10 emeralds and 1 book. An odd trade to be sure, but it works.

I know you've probably either given up or found a work around by now, but this is for those who stumble across this question/answer later.

You can't make them stop spawning in new trades, I made a lucky block that spawns a lucky villager but he keeps leveling up his trades.

Use entitydata each time player is traded using scoreboard of stat.tradedWithVillager to reset the trade of the villager. It could lag if there is too much villager, but I think this is the best way to prevent from new trade.

One of you said that the max career level is 4, so I used this command

/summon Villager ~ ~1 ~ {Profession:0,Career:2,CareerLevel:4,Offers:{Recipes:[{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:8,tag:{display:{Name:"Coin"}}},sell:{id:wooden_sword,Count:1,tag:{Unbreakable:1,display:{Name:"Sturdy Stick"}}}},{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:12,tag:{display:{Name:"Coin"}}},sell:{id:golden_sword,Count:1,tag:{AttributeModifiers:[{AttributeName:"generic.movementSpeed",Name:"generic.movementSpeed",Amount:-.10,Operation:1,UUIDLeast:112181,UUIDMost:524106}],Unbreakable:1,ench:[{id:16,lvl:1}]}}},{rewardExp:0b,maxUses:2147483647,uses:0,buy:{id:double_plant,Count:2,tag:{display:{Name:"Coin"}}},sell:{id:leather,Count:1}}]},Attributes:[{Name:generic.movementSpeed,Base:0}],PersistenceRequired:1,ActiveEffects:[{Id:10,Amplifier:50,Duration:133333333333320,ShowParticles:0b},{Id:21,Amplifier:60,Duration:1333333333333333200}]} 

and set the career level at 4, this spawns a villager with a career level of 4 that will trade sunflowers named Coin for certain items. Now I tested this multiple times to make sure I was correct, and I was, setting the career level at 4 will prevent new trades from appearing. I am not sure if this works in 1.9, 1.10 or 1.11 because I still play in 1.8.9.