Po skończeniu kolacji teść podał mi herbatę, a teściowa przyniosła jeszcze kawałek sernika.

It is a time expression meaning after finishing dinner or after the dinner was finished.

Grammatically, it is built with:

• po = after
• skończeniu = the finishing / completion
• kolacji = of dinner

So the whole phrase literally has the structure after the completion of dinner.

In natural English we would usually translate it more smoothly, but in Polish this is a very normal way to express after doing something.

Because the preposition po normally requires the locative case when it means after.

So:

• base form: skończenie
• locative after po: skończeniu

That is why you get po skończeniu.

This pattern is very common:

• po obiedzie = after lunch
• po pracy = after work
• po przyjeździe = after arriving
• po skończeniu lekcji = after finishing class

Because skończenie is a verbal noun derived from skończyć (to finish), and it keeps the logic of the verb.

With the verb, you say:

• skończyć kolację = to finish dinner

But with the noun skończenie, Polish commonly uses the genitive for the object:

• skończenie kolacji = the finishing of dinner

So:

• po skończeniu kolacji = after the finishing of dinner

This is a very common pattern with verbal nouns in Polish.

Here the verb podać takes:

• a direct object in the accusative: herbatę
• an indirect object in the dative: mi

So:

• herbata → herbatę because it is the thing being served/handed
• ja → mi because it means to me

The structure is:

• teść podał mi herbatę = father-in-law served/handed me tea

This is very typical Polish case usage:

• dał mi książkę = he gave me a book
• pokazała mi zdjęcie = she showed me a photo
• przyniósł mi kawę = he brought me coffee

Mi is the normal short, unstressed dative form of I / me in sentences like this.

So Polish usually prefers:

• podał mi herbatę
• dał mi książkę
• powiedział mi prawdę

The longer form mnie is used when you want emphasis, contrast, or after some prepositions.

For example:

• Mnie podał herbatę, a nie tobie. = He served tea to me, not to you.
• dla mnie = for me

So in your sentence, mi is the natural neutral choice.

They are similar, but not identical.

• podał means handed, served, or passed
• przyniosła means brought

So the idea is slightly different:

• teść podał mi herbatę = he served or handed me the tea
• teściowa przyniosła jeszcze kawałek sernika = she brought another piece of cheesecake

This sounds very natural, because tea is something you might serve/hand to someone, while cake is something you might bring from the kitchen or from the table.

Yes. Both are perfective past-tense forms:

• podał ← podać
• przyniosła ← przynieść

Perfective verbs are used here because the sentence describes completed, one-time actions in a sequence:

1. dinner was finished
2. father-in-law served tea
3. mother-in-law brought another piece of cheesecake

If you used imperfective forms such as podawał or przynosiła, it would suggest repeated action, ongoing action, or a different narrative focus.

So the perfective forms fit a simple completed event very well.

Here jeszcze means something like another, one more, or an additional.

So:

• jeszcze kawałek sernika = another piece of cheesecake / one more piece of cheesecake

This is a very common use of jeszcze in offering food or drink:

• Chcesz jeszcze kawy? = Do you want some more coffee?
• Weź jeszcze ciasto. = Have another piece of cake.
• Przyniosę jeszcze jedną szklankę. = I’ll bring one more glass.

So in this sentence, jeszcze does not mean only still. It means more / additional.

Because after kawałek (a piece / a bit), Polish normally uses the genitive.

So:

• kawałek czego? = a piece of what?
• sernika = of cheesecake

That is why you get:

• kawałek sernika

The same pattern appears in many similar expressions:

• kawałek chleba = a piece of bread
• szklanka wody = a glass of water
• trochę mleka = a bit of milk
• kilogram jabłek = a kilogram of apples

So sernika is genitive because it depends on kawałek.

In Polish, a often links two clauses while also showing a contrast, switch, or change of topic/subject.

Here the sentence moves from one person to another:

• teść podał mi herbatę
• a teściowa przyniosła jeszcze kawałek sernika

So a feels very natural because it means something like:

• and meanwhile
• and as for
• while
• sometimes just a slightly contrastive and

If you used i, the sentence would still be understandable, but a is more natural when you are contrasting or pairing two different people doing two different things.

Yes, absolutely.

• po kolacji = after dinner
• po skończeniu kolacji = after finishing dinner / after the dinner was finished

The shorter version, po kolacji, is simpler and very common.

The longer version, po skończeniu kolacji, puts a little more focus on the idea that the meal had been completed. It is slightly more explicit, but still perfectly natural.

So both are correct; the version in your sentence is just a bit more detailed.