Po badaniu lekarz mówi, że moje ciśnienie jest trochę za niskie.

Because the preposition po usually takes the locative case when it means after.

• badanie = examination, test
• po badaniu = after the examination

So:

• nominative: badanie
• locative: badaniu

This is a very common pattern:

• po obiedzie = after lunch
• po pracy = after work
• po spotkaniu = after the meeting

Here po means after.

So Po badaniu means After the examination or Following the examination.

Be careful: po can mean different things in other contexts, for example:

• po polsku = in Polish
• iść po chleb = go to get bread
• po stole = along/on the table

But in this sentence, it clearly means after.

Polish does not have articles like a or the.

So lekarz can mean:

• a doctor
• the doctor

The context tells you which one is meant. In this sentence, English naturally translates it as the doctor because it is the doctor connected with the examination.

There are two separate points here:

1. mówi
   This is the present tense: says / is saying.

   • lekarz mówi = the doctor says

   If you used powiedział, that would mean said in the past:

   • Po badaniu lekarz powiedział... = After the examination, the doctor said...

2. comma before że
   In Polish, a comma is normally placed before że when it introduces a subordinate clause.

So:

• Lekarz mówi, że... = The doctor says that...

That comma is standard and important in Polish spelling.

że means that and introduces a subordinate clause.

• Lekarz mówi, że moje ciśnienie jest...
• The doctor says that my blood pressure is...

In English, that is often optional:

• The doctor says my blood pressure is...

In Polish, że is normally expressed in this kind of sentence.

Because ciśnienie is a neuter noun, and the possessive adjective my must agree with it.

• masculine: mój
• feminine: moja
• neuter: moje

So:

• mój samochód = my car
• moja książka = my book
• moje ciśnienie = my blood pressure

This agreement is very important in Polish.

Because the adjective must agree with ciśnienie, which is neuter singular.

• ciśnienie = neuter singular
• therefore niskie = neuter singular form of niski (low)

Compare:

• wysoki chłopiec = a tall boy
• wysoka dziewczyna = a tall girl
• wysokie drzewo = a tall tree

Here:

• ciśnienie jest niskie = the blood pressure is low

No. In this sentence, za means too.

So:

• niskie = low
• za niskie = too low

This is a very common structure:

• za drogie = too expensive
• za późno = too late
• za mały = too small

So jest za niskie means is too low.

trochę means a little, a bit, or somewhat.

So:

• za niskie = too low
• trochę za niskie = a little too low / slightly too low

It softens the statement. The doctor is not saying the blood pressure is dangerously low, just that it is somewhat below the ideal level.

By itself, ciśnienie means pressure in a general sense. But in medical context, moje ciśnienie usually means my blood pressure.

Examples:

• ciśnienie krwi = blood pressure
• wysokie ciśnienie = high blood pressure
• niskie ciśnienie = low blood pressure

So in this sentence, even though krwi is not stated, the meaning is clearly blood pressure.

Yes, Polish word order is more flexible than English, although some versions sound more natural than others.

The given sentence:

• Po badaniu lekarz mówi, że moje ciśnienie jest trochę za niskie.

is completely natural.

You could also say:

• Lekarz po badaniu mówi, że moje ciśnienie jest trochę za niskie.
• Lekarz mówi po badaniu, że moje ciśnienie jest trochę za niskie.

But these may shift emphasis slightly.

Polish often uses word order for focus rather than strict grammar. Still, the original version is a very normal way to present the situation: first the time/context (after the examination), then the main action.

A rough English approximation is cheesh-NYE-nyeh.

More precisely:

• ci before ś sounds like a soft ch / ć-like sound
• ś is a soft sh
• nie here sounds like nye

So the whole word is pronounced something like:

• ciśnienie ≈ cheesh-NYE-nye

If it helps, you can break it up like this:

• ciś-nie-nie

This is one of those Polish words that looks intimidating at first, but becomes easier once you recognize common soft consonant patterns.

jest is the 3rd person singular form of być = to be.

So:

• ciśnienie jest niskie = the blood pressure is low

In present-tense equational/descriptive sentences, Polish often uses jest just like English uses is.

Here:

• moje ciśnienie jest trochę za niskie
• my blood pressure is a little too low

So jest links the subject (moje ciśnienie) with the description (trochę za niskie).