Mi treniramo u dvorani, a ostali treniraju u parku.

Yes, mi can be left out here.

• Mi treniramo u dvorani = Treniramo u dvorani
  Both mean We train in the hall / gym.

Croatian verb endings already show the person:

• treniramo clearly shows 1st person plural (we)

So the full sentence without mi would be:

• Treniramo u dvorani, a ostali treniraju u parku.

Using mi just emphasizes we a bit more (e.g. in contrast to others).

They are different present tense forms of the verb trenirati (to train):

• treniramo = we train (1st person plural)
• treniraju = they train (3rd person plural)

Present tense of trenirati:

• ja treniram – I train
• ti treniraš – you (sg) train
• on/ona/ono trenira – he/she/it trains
• mi treniramo – we train
• vi trenirate – you (pl/formal) train
• oni/one/ona treniraju – they train

So the verb changes instead of adding a subject pronoun like in English.

Dvorana is a feminine noun:

• base form (nominative singular): dvorana – hall / sports hall

After the preposition u meaning in (location, static place), Croatian uses the locative case.
For feminine nouns like dvorana, the locative singular ending is usually -i:

• u dvorani = in the hall / in the gym

So:

• dvorana (dictionary form, subject)
• u dvorani (in the hall – locative, after u for location)

Park is a masculine noun:

• base form (nominative singular): park

Again, u with a static location uses the locative case.
For many masculine nouns ending in a consonant, the locative singular ending is -u:

• u parku = in the park

So:

• park (dictionary form)
• u parku (in the park – locative singular)

Yes, both are locative.

The preposition u can take different cases, but a simple rule:

• u
  • locative = in (location, being inside somewhere)
    
    • u dvorani – in the hall
    • u parku – in the park
• u
  • accusative = into (movement into somewhere)
    
    • Idemo u dvoranu. – We’re going into the hall.
    • Idem u park. – I’m going to the park.

In your sentence, the meaning is where the training happens (location), so locative is used.

Croatian has no articles (no words like a / an / the).

• u dvorani can be translated as in a hall, in the hall, or in the gym, depending on context.
• u parku can be in a park or in the park.

Context and previous mention usually tell the listener whether you mean a or the. The Croatian form itself does not change.

Ostali means the others / the rest.

• Mi treniramo u dvorani, a ostali treniraju u parku.
  = We train in the hall, and the others train in the park.

Details:

• ostali is the masculine plural form (it agrees with an implied masculine or mixed group plural noun, like ljudi – people).
• It has a nuance of the remaining ones / everyone else.

Drugi can also mean other, but:

• ostali = the rest of the group you’re talking about
• drugi = other / another, more general, can also mean second in some contexts

Here ostali is more natural because it contrasts “we” with “everyone else” in that group.

Yes, that’s also correct, but the meaning is slightly different:

• Mi treniramo u dvorani, a oni treniraju u parku.
  = We train in the hall, and they train in the park.
  (just we vs they, two groups)

• Mi treniramo u dvorani, a ostali treniraju u parku.
  = We train in the hall, and the others train in the park.
  (we are part of a larger group, and the rest train somewhere else)

Oni just refers to another group; ostali implies “all the remaining members of the same broader group.”

Both a and i can be translated as and, but they’re used differently:

• i = simple addition, like and

  • Mi treniramo u dvorani i treniramo u parku.
    (We train in the hall and train in the park – just adding information.)

• a = and / while / whereas / but in a contrasting sense
  It often contrasts two subjects or situations.

In your sentence:

• Mi treniramo u dvorani, a ostali treniraju u parku.
  = We train in the hall, while / whereas the others train in the park.

So a emphasizes the contrast between mi and ostali, and between u dvorani and u parku.

Yes, Croatian word order is flexible, and that version is grammatically correct:

• U dvorani mi treniramo, a u parku treniraju ostali.

The basic meaning is the same, but emphasis shifts:

• Mi treniramo u dvorani, a ostali treniraju u parku.
  → more neutral; slight focus on who does what.

• U dvorani mi treniramo…
  → emphasizes the place first: In the hall, we train…

• …a u parku treniraju ostali.
  → again focuses on the place first: and in the park, the others train.

Croatian uses word order partly for emphasis rather than strict grammar.

In this sentence, no: Mi treniramo u dvorani is correct and natural.

• trenirati can be:
  • intransitive: Mi treniramo. – We train / practice.
  • transitive: Mi treniramo nogomet. – We train football.

Se treniramo would sound wrong or at least very unusual here.
You might see forms like trenirati se in certain expressions, but for we train (work out / practice), just treniramo is used.

Trenirati is usually used as an imperfective verb in modern Croatian.

• Mi treniramo u dvorani describes an ongoing, habitual, or repeated action:
  We train / we are training in the hall.

There is a perfective partner istrenirati (to train up, to train fully), but:

• You would not use istreniramo in this sentence, because you’re not describing a completed one-time result, but a regular or ongoing activity.

So treniramo here is imperfective present.