Learn Hardcore Polish: My biegamy regularnie w parku.

mój – my (masculine singular noun)
- mój pies – my dog
moja – my (feminine singular noun)
- moja książka – my book
moje – my (neuter singular noun)
- moje dziecko – my child
moi / moje / moje – my (plural forms, depending on gender)
- moi przyjaciele – my (male/mixed) friends
- moje koleżanki – my (female) friends

So English my ≠ Polish my. They are false friends.

If biegamy already means we run, do we really need to say my? When would you include or omit my?

You do not need to say my here. The verb ending -my already tells you the subject is we.

Biegamy regularnie w parku. – perfectly natural, neutral sentence.
My biegamy regularnie w parku. – grammatically correct, but adds emphasis to we.

You add my mainly for:

Contrast / emphasis
- My biegamy regularnie w parku, a oni tylko czasem.
  We run regularly in the park, but they only sometimes.
Clarity in complex contexts
When several people are being discussed and you want to highlight the subject.

In everyday speech, Poles usually drop subject pronouns unless they want that emphasis. So the more natural version is:

Biegamy regularnie w parku.

What is the difference in meaning or feel between My biegamy regularnie w parku and Biegamy regularnie w parku?

The meaning (who does what, where, how often) is the same. The feel is different:

Biegamy regularnie w parku.
Neutral, factual: We run regularly in the park.
My biegamy regularnie w parku.
Emphasises we. It sounds a bit like:
- We (as opposed to others) run regularly in the park.
- Or: At least we run regularly in the park.

So My adds a slight contrast or focus on the subject.

Why is regularnie after biegamy? Can I move regularnie to another place in the sentence?

Regularnie is an adverb (regularly). The most neutral place for adverbs of frequency in Polish is after the verb:

Biegamy regularnie w parku. – very natural.

You can move it, but the tone or focus changes slightly:

Regularnie biegamy w parku.
Focus on regularnie – you stress the fact that it is regular.
Biegamy w parku regularnie.
Also possible; not wrong, but a bit less typical and can sound slightly more marked.
My regularnie biegamy w parku.
Stronger emphasis both on we and regularly.

All of these are grammatical. For everyday use, Biegamy regularnie w parku is the most neutral and common.

Why is it w parku and not w park? What case is used after w here?

Polish prepositions change the case of the noun that follows. The preposition w can take:

Locative case – for being in/inside/at a place
Accusative case – for movement into something (though with park you would more often see do parku for into the park)

Your sentence describes where the action happens (location), not movement into somewhere, so w needs the locative case:

base form: park (nominative)
locative singular: parku

Therefore:

w parku = in the park

If you talked about going into the park, you would typically say:

Idziemy do parku. – We are going to the park.
(not w parku, because that is location, not destination)

What exactly is parku? How does park change to parku?

Park is a masculine inanimate noun. Its dictionary (base) form is park (nominative singular).

Its main singular forms:

Nominative (who? what?): park – To jest park. (This is a park.)
Genitive (of…?): parku – nie ma parku (there is no park)
Dative (to…?): parkowi
Accusative (what?): park – widzę park (I see the park)
Instrumental (with…?): parkiem
Locative (in/at…?): parku – w parku (in the park), o parku (about the park)

In your sentence, w requires the locative, so park changes to parku:

w
- park → w parku (in the park)

Does biegamy mean we run (in general) or we are running (right now)? How does Polish express this?

Polish has one present tense form, but it uses verb aspect and different verb stems to show the difference you feel in English.

Biegamy comes from biegać and usually means:

we run / we go running (habitually, regularly, as an activity)

So Biegamy regularnie w parku is naturally understood as a habit or routine.

For we are running (right now, in one direction) you more often use:

Biegniemy (from biec):
- Teraz biegniemy w parku. – Right now we are running in the park.

Summary:

biegamy – we (tend to) run / we run around, habitually, repeatedly
biegniemy – we are running (right now, usually in some direction)

Why are there different verbs like biegać and biec for to run? Which one am I using in biegamy?

In your sentence, biegamy is from biegać.

Polish has a somewhat richer system for motion verbs. For to run, the most important for you now are:

biegać – to run (around), to go running, to run as a habit
- Biegamy regularnie w parku. – We run regularly in the park.
biec – to run (in one direction, specific movement)
- Biegniemy do domu. – We are running home.

Later you will also meet perfective forms like:

pobiec – to run off / to run (once, until a certain point)
dobiec – to run (up to / reach somewhere), etc.

For general statements like we run regularly, biegać (so biegamy) is the right choice.

How do you pronounce My biegamy regularnie w parku?

Approximate pronunciation (stressed syllables in CAPS):

My – /mɨ/ – like m
- short i in bit, but more central
biegamy – /bʲeˈɡamɨ/ – bye-GA-mih (but bye is short, not like English bye)
regularnie – /rɛɡuˈlarnʲɛ/ – reh-goo-LAR-nyeh
w parku – /f ˈparku/ – f PAR-koo

Full sentence (very approximate English-like rendering):

mɨ bye-GA-mih reh-goo-LAR-nyeh f PAR-koo

Key points:

Stress in Polish is almost always on the penultimate (second-from-last) syllable:
bie–GA–my, re–gu–LAR–nie.
my is not like English my; it is more like mih or mɨ.
w before p is pronounced like f, so w parku sounds like f parku.

Why does w in w parku sound like f?

This is due to voicing assimilation, a common feature in Polish.

The preposition w on its own is voiced /v/.
But in w parku, the next consonant p is voiceless.
Polish tends to make neighbouring consonants match in voicing, so /v/ becomes /f/ before p.

So:

written: w parku
pronounced: [f parku]

The same happens in other combinations:

w sklepie – pronounced like f sklepie
w szkole – pronounced like f szkole

Can I change the word order, for example say W parku biegamy regularnie or Regularnie biegamy w parku? Does it change the meaning?

Yes, Polish word order is fairly flexible, and all of these are grammatical:

Biegamy regularnie w parku.
Neutral, most typical.
Regularnie biegamy w parku.
Emphasises regularnie a bit more: It is regularly that we run in the park.
W parku biegamy regularnie.
Emphasises w parku (the place): In the park we run regularly (as opposed to somewhere else).
My biegamy regularnie w parku.
Emphasis on we (contrast with others).

The core meaning stays the same, but the focus of the sentence shifts depending on what you put first. For everyday use, Biegamy regularnie w parku is the safest, neutral default.