Using simple past with and without specific time

You 3 sentences are grammatically correct. However, they do not really make much sense, because there is no context. Generally speaking, any statement without its context will sound 'weird' because it will not relate to anything the receiver knows. Example:

A - I ate an apple.

B - Huh, what are you talking about?

A - You asked me if I was hungry. No, I'm not, I ate an apple 10 minutes ago.

B - Okay.

The time marker may not be present in the sentence itself, but it has to be mentioned somewhere before, so as to prevent any misunderstanding.

The key to your question lies in the duration of that action, even in the past.

All of the actions you've mentioned terminate in the telling (that is they took place, and have now finished by the time you're reporting it).

I went to the beach.

I ate an apple.

We won several medals.

No one would ever confuse these items as things that were ongoing in the past for a time period. You weren't continuously going to the beach, eating an apple, or winning the medals.

By comparison consider the following sentences:

I was at the beach.

I was eating an apple.

I was competing, hoping to win several medals.

Notice how each of these examples don't seem to have an end point that is readily apparent? You were at the beach, eating an apple, competing. Essentially all of these actions took place in the past, but they were ongoing at this point in your telling.

These are examples of the imperfect tense to the degree that English has one. Unlike most other languages, English doesn't have quite such hard and fast rules regarding conjugation and tense.

So, when do you use the simple past vs the imperfect? An easy (but not unbreakable) rule is this:

If you're describing an action that was already done at the time of telling, use the simple past.

If you're describing and action that was ongoing when your telling takes place, then use the imperfect. This is especially true when you're trying to indicate an action was ongoing while performing another action:

I was at the beach and I ate an apple.

Note the mix of the imperfect and simple past here. The apple was eaten (finite action) while I was sitting at the beach (ongoing in the past).

Habits are tricky.

I ran five miles per day.

This can be either tense and you need context to decipher it.

I ran five miles per day (while I was on vacation).

Simple past.

I ran five miles per day (back when I was young).

Probably the imperfect, though you could make a case for this being the simple past.

No, there's nothing that states, "...you must use a specific time for the first use to be grammatically correct," not even your link, which states, "The simple past... is used to show that a completed action took place at a specific time in the past." That doesn't say that specific time in the past has to actually be explicated. You don't have to say when that specific time in the past was to use the simple past, and when you leave it unstated, then the simple past nonetheless conveys or shows that that specific time in the past exists.

It's actually explained in the link you provided: https://www.englishpage.com/verbpage/simplepast.html

Sometimes, the speaker may not actually mention the specific time, but they do have one specific time in mind.

Example given is:

She washed her car.