Czekam siedem dni.

Czekam is the 1st person singular present-tense form of czekać (to wait).

So:

• czekam = I wait / I am waiting
• the ending -am already tells you the subject is I

That is why Polish does not need a separate word for I here.

Because Polish verb endings usually show the subject clearly.

In czekam, the ending tells you it means I am waiting, so ja is unnecessary.

You can say Ja czekam siedem dni, but that adds emphasis, as if you were contrasting yourself with someone else:

• Ja czekam siedem dni, a on tylko dwa.
  I’ve been waiting seven days, and he only two.

In a neutral sentence, Czekam siedem dni is more natural.

It is a duration expression meaning for seven days.

With Polish numerals:

• after 5 and higher, the noun normally appears in the genitive plural
• dzień (day) has genitive plural dni

So:

• siedem dni = seven days

A useful detail: the whole phrase works as a time-span expression after the verb, even though the noun itself is in the plural form required by the numeral.

Because dzień is singular: day. After siedem (seven), Polish needs the plural quantity form.

So:

• dzień = day
• dni = days

You cannot say siedem dzień.

Also, dzień is a slightly irregular noun, so its plural is dni, not something more predictable like dzieńe or dzienie.

Polish often expresses duration without a preposition.

So English:

• I have been waiting for seven days

can be expressed in Polish as:

• Czekam siedem dni

Literally, it looks like I am waiting seven days, but in Polish that direct time expression is normal.

Yes, when you say what or who you are waiting for, you normally use na:

• Czekam na autobus. = I’m waiting for the bus.
• Czekam na Annę. = I’m waiting for Anna.

But siedem dni is not the thing you are waiting for. It tells you how long the waiting lasts. That is why there is no na here.

You can combine both:

• Czekam na autobus siedem dni. More naturally:
• Już siedem dni czekam na autobus.

Because Polish often uses the present tense of an imperfective verb for an action that:

• started earlier
• is still continuing now

So Czekam siedem dni can correspond to English:

• I have been waiting for seven days

This is very normal in Polish. English prefers the present perfect continuous, while Polish often just uses the present.

It is grammatical, but by itself it can sound a little bare.

In everyday Polish, if you mean I have already been waiting for seven days, people often add już:

• Czekam już siedem dni.

That sounds more natural in many contexts, because już makes the ongoing duration clearer.

Very often Polish would also include what the speaker is waiting for:

• Czekam na odpowiedź już siedem dni.
  I’ve been waiting for an answer for seven days already.

Yes. Polish word order is fairly flexible, and changing it changes the emphasis more than the core meaning.

For example:

• Czekam siedem dni. = neutral
• Siedem dni czekam. = emphasis on seven days
• Już siedem dni czekam. = emphasis on already seven days
• Czekam już siedem dni. = very natural everyday order

So the sentence can move around depending on what you want to stress.

A rough pronunciation guide:

• czekam ≈ CHE-kam
• siedem ≈ SHYE-dem or more accurately ŚE-dem
• dni = one syllable, roughly dnyi

IPA:

• czekam — [ˈt͡ʂɛ.kam]
• siedem — [ˈɕɛ.dɛm]
• dni — [dɲi]

A few helpful points:

• cz sounds like English ch in chop, but harder
• si before e sounds like a soft ś
• dni is compact and can be tricky for English speakers because of the dń cluster

You can change the tense like this:

• Czekałem siedem dni. / Czekałam siedem dni.
  I waited for seven days.
  Masculine speaker: czekałem
  Feminine speaker: czekałam

• Będę czekać siedem dni.
  I will wait for seven days.

A very common future alternative is with the perfective verb:

• Poczekam siedem dni.
  I’ll wait seven days.

So:

• czekam = I am waiting / I have been waiting
• czekałem / czekałam = I waited
• będę czekać / poczekam = I will wait