That's because Romanian is a Romance language, descended from Vulgar Latin after the Roman colonization of present-day Romania.

Both are (through intermediaries at least in the case of English) coming from the latin prefix "in-" and "bracchia" (arm).

Also compare to modern Italian "abbracciare".

Yes, that is the same root.

Just as a side note, 'brace' here (brațe in Romanian, braccia in Italian) is simply the word for arms (as in hands, not as in swords), so the word in romance languages sounds essentially like 'enarm' would in English (without the weapon connotation).