Po czternastu dniach mam odpowiedź.

Because the preposition po here means after, and in this meaning it requires the locative case.

So both words change form:

• czternaście → czternastu
• dni / dictionary form dzień → dniach

That is why you get:

• po czternastu dniach = after fourteen days

Using po czternaście dni would be ungrammatical in this sentence.

Because Polish numerals can decline too, just like nouns and adjectives.

Here the numeral is part of a phrase governed by po, which requires the locative. So czternaście takes its locative form:

• nominative: czternaście
• locative: czternastu

This is very common after prepositions that require a specific case.

Because dzień is being used in the locative plural after po.

The forms are:

• singular nominative: dzień = day
• plural nominative: dni = days
• locative plural: dniach

So:

• po dniu = after a day
• po dwóch dniach = after two days
• po czternastu dniach = after fourteen days

This noun is a little irregular, so it is worth memorizing its common forms:

• dzień
• dnia
• dni
• dniach

Because the sentence refers to fourteen days, so Polish uses a plural time noun here.

With larger numbers, Polish often uses forms that do not work like English. In this sentence, because the whole phrase is in the locative plural, the noun appears as dniach.

So the idea is literally:

• after fourteen days

not after fourteen day.

It is in the accusative singular, because it is the direct object of mam (I have).

However, for this noun, the nominative and accusative forms look the same:

• nominative: odpowiedź
• accusative: odpowiedź

So even though the form does not change, the function does.

Literally, mam odpowiedź means I have an answer.

In context, Polish sometimes uses mam in situations where English might say:

• I have the answer
• I get the answer
• I receive an answer

But grammatically, mam is simply the present tense of mieć = to have.

A more explicitly receive-type sentence would be:

• Po czternastu dniach dostaję odpowiedź.
• Po czternastu dniach otrzymuję odpowiedź.

So mam odpowiedź focuses on possessing/having the answer, not the act of receiving it.

Yes. Polish word order is flexible.

You could say:

• Po czternastu dniach mam odpowiedź.
• Mam odpowiedź po czternastu dniach.

Both are grammatical, but they emphasize slightly different things.

• Po czternastu dniach mam odpowiedź.
  This puts the time phrase first, so it highlights when.
• Mam odpowiedź po czternastu dniach.
  This starts with I have an answer, so it highlights the result more.

In neutral usage, the original sentence sounds natural.

Yes. In everyday writing, Po 14 dniach is completely normal.

When reading it aloud, though, you would still say:

• po czternastu dniach

So the number version and the fully written version mean the same thing.

These are related, but not the same.

• po czternastu dniach = after fourteen days
• za czternaście dni = in fourteen days

Very often, in real-life contexts, they can point to the same time frame, but the perspective is different:

• po czternastu dniach looks at what happens after a period has passed
• za czternaście dni points forward from now to a future moment

Examples:

• Po czternastu dniach mam odpowiedź. = After fourteen days, I have an answer.
• Za czternaście dni będę miał odpowiedź. = In fourteen days, I will have an answer.

Yes, po has several meanings in Polish. Its meaning depends on context.

Here, with a time expression, po means:

• after

So:

• po obiedzie = after lunch
• po pracy = after work
• po czternastu dniach = after fourteen days

In other contexts, po can mean things like:

• along
• around
• for
• by

But in this sentence it is clearly a time expression meaning after.

Because Polish has no articles like English a/an/the.

So odpowiedź can mean:

• an answer
• the answer

You understand which one is meant from context.

That is why mam odpowiedź could be interpreted as:

• I have an answer
• I have the answer

depending on the situation.

Because Polish usually does not need subject pronouns unless you want emphasis or contrast.

The verb form mam already tells you the subject is I.

• mam = I have

So ja is normally omitted.

You would include ja only if you want emphasis, for example:

• Ja mam odpowiedź, a ty nie.
  I have the answer, and you do not.

Grammatically, mam is present tense: I have.

But depending on context, a present-tense Polish sentence can sometimes refer to a future result, especially in practical or scheduled situations.

So the sentence may be understood as:

• After fourteen days, I have an answer or more naturally in English,
• After fourteen days, I’ll have an answer

This depends on the wider context, not just the grammar of the sentence itself.