Learn Hardcore Indonesian: Kami bekerja seharian, tetapi istirahat sebentar sebelum pulang. - We worked all day, but took a short break before going home.

So kami implies the speaker’s group worked, but the person being addressed was not part of that group. If you are talking to teammates who also worked, use kita.

Do I need to repeat the subject in the second clause (before istirahat)?

No. Indonesian often drops the repeated subject when it’s the same as in the previous clause. All are acceptable:

Kami bekerja seharian, tetapi istirahat sebentar sebelum pulang. (natural, concise)
Kami bekerja seharian, tetapi kami beristirahat sebentar sebelum pulang. (also correct; heavier, adds emphasis/clarity)

Should it be istirahat or beristirahat?

Both are correct. Istirahat can function as a verb (to rest) or a noun (a rest). Beristirahat is the more overtly verbal/standard form and feels a bit more formal. In everyday speech and writing, istirahat on its own is very common:

Kami istirahat sebentar. (very common)
Kami beristirahat sebentar. (a bit more formal)

What exactly does sebentar mean? Are there alternatives?