U kabini mi je pretoplo, ali veličina jakne je dobra.

Because u + locative is used for location (where?): U kabini = in the fitting room/cabin.
U + accusative is used for movement (to where?): U kabinu = into the fitting room/cabin (entering it).

kabini is locative singular of kabina (feminine noun).
Typical locative ending for many feminine nouns is -i: kabina → (u) kabini.

This is an impersonal “feels like” type construction: mi is dative meaning to me / for me, and je is is.
So mi je pretoplo literally means it is too warm to/for me → “I’m too hot / it’s too warm for me (in there).”

Yes. meni is the stressed/full form, used for emphasis or contrast.

• Neutral: U kabini mi je pretoplo.
• Emphatic/contrastive: U kabini meni je pretoplo (a tebi nije). = “In the fitting room, I’m too hot (but you aren’t).”

Here pretoplo functions as a predicative adjective/adverb-like form (often called a “state” expression): (it is) too warm.
The -o is the neuter form used in impersonal statements like:

• Hladno je. = “It’s cold.”
• Vruće je. = “It’s hot.”
• Pretoplo je. = “It’s too warm.”

Both mean too hot/too warm, but the nuance differs:

• pretoplo = “too warm” (often slightly milder or more “warmth” oriented)
• prevruće = “too hot” (more “heat” intense)
  In everyday speech, both are common and often interchangeable.

Croatian word order is flexible, but clitics like mi and je have strong placement rules: they usually come early in the clause (often in “second position”).
Starting with U kabini sets the scene (“in the fitting room”), then the clitic cluster mi je follows naturally: U kabini | mi je | pretoplo.
You can move u kabini later for emphasis, but it may sound more marked: Mi je pretoplo u kabini (less neutral).

Because there are two separate clauses, each with its own predicate:
1) mi je pretoplo = “it’s too warm for me”
2) veli​ភina jakne je dobra = “the jacket size is good”
In casual speech, the second je is often dropped: ... ali veličina jakne dobra. (still common and natural).

jakne is genitive singular of jakna (“jacket”).
It’s used because veliči­na (“size”) is typically expressed as X of Y → veliči­na jakne = the jacket’s size / the size of the jacket.

It can cover both, but in this sentence it most naturally means the jacket’s size / the size (fit) of the jacket is good—i.e., the size you chose fits well.
If you wanted to stress the labeled size, you might add context, e.g. Broj jakne je dobar (“the size number is good”) in some varieties.

Because dobra agrees with veliči­na, which is feminine singular.
Adjective agreement in Croatian matches gender + number + case:

• veliči­na (fem. sg.) → dobra (fem. sg.)
  If it were a neuter noun, you’d use dobro, e.g. mjesto je dobro (“the place is good”).