Poczekaj przy wejściu, aż przestanę szukać kluczy w torbie.

Both can translate as wait, but they are different in aspect.

Poczekaj comes from the perfective verb poczekać and suggests waiting up to some point or for some completed stretch of time. That fits very well with aż... = until...

Czekaj comes from the imperfective verb czekać and sounds more like be waiting, keep waiting, or wait as an ongoing activity.

In this sentence, Poczekaj is more natural because the sentence has a clear endpoint: until I stop looking for the keys.

It is informal singular: you say it to one person you address with ty.

If you wanted to be formal, you would usually say something like:

Proszę poczekać przy wejściu, aż przestanę szukać kluczy w torbie.

If you were speaking to more than one person informally, you would use:

Poczekajcie...

Polish usually does not need subject pronouns when the verb ending already shows who is doing the action.

Przestanę means I will stop. The ending -ę tells you it is I.

So Polish often omits ja unless you want emphasis or contrast. For example:

Ja przestanę, ale on nie.
= I will stop, but he will not.

In your sentence, ja would be unnecessary.

Przy wejściu means by the entrance, at the entrance, or near the entrance.

The preposition przy takes the locative case, so wejście changes to wejściu.

Basic pattern:

• wejście = entrance
• przy wejściu = at/by the entrance

So this is a normal preposition + case combination you just have to learn:

• przy
  • locative

Here aż means until.

It introduces the point in time up to which the waiting continues:

Poczekaj przy wejściu, aż przestanę...
= Wait by the entrance until I stop...

In other contexts, aż can have other meanings, but in this sentence it is simply the conjunction until.

Przestanę means I will stop.

It comes from the perfective verb przestać. In Polish, perfective verbs do not normally have a true present-tense meaning. Their present-style forms usually refer to the future.

So:

• przestaję = I am stopping / I stop
• przestanę = I will stop

In this sentence, the future meaning is needed, because the stopping happens after the speaker says this.

Because przestać is commonly followed by an infinitive when you say what action stops.

So:

• przestanę szukać = I will stop looking
• przestań mówić = stop talking
• przestał padać = it stopped raining

This is a very common Polish pattern:

przestać + infinitive

Because the verb szukać takes the genitive case, not the accusative.

So:

• klucze = nominative/accusative plural
• kluczy = genitive plural

After szukać, you say:

• szukać kluczy = to look for keys

Compare:

• Mam klucze. = I have the keys / I have keys.
• Szukam kluczy. = I am looking for the keys / for keys.

This is one of those verbs whose object case must be memorized.

Because w meaning in for location takes the locative case.

So:

• torba = bag
• w torbie = in the bag

This means the keys are being searched for in the bag.

A useful contrast:

• w torbie = in the bag, located there
• do torby = into the bag, movement toward the inside

Because aż przestanę szukać kluczy w torbie is a subordinate clause.

In Polish, subordinate clauses are normally separated by a comma, including clauses introduced by aż.

So the comma here is standard and correct: Poczekaj przy wejściu, aż przestanę szukać kluczy w torbie.

Yes, Polish word order is flexible, but not completely free. The original sentence is very natural and neutral.

Poczekaj przy wejściu, aż przestanę szukać kluczy w torbie.

You could also say: Przy wejściu poczekaj, aż przestanę szukać kluczy w torbie.

That puts a little more emphasis on przy wejściu.

But you should be careful not to move words so much that the sentence becomes awkward or changes what seems to belong together. For example, szukać kluczy w torbie naturally stays together because in the bag describes where the search is happening.

Yes, you could, but the nuance changes slightly.

• przestanę szukać = I will stop looking
• skończę szukać = I will finish looking

Skończę sounds more like the action reaches its end naturally.
Przestanę focuses on the stopping itself and can sometimes suggest giving up, interrupting the action, or simply ceasing it for whatever reason.

In everyday speech, both can work, but they are not always identical in tone.