What difference in the pronunciation would it do if you replaced 'or' by 'and'? Are you happy and are they happy?
"And" is never "o". It can be "u" in some situations, although colloquially it is always "ve".
In formal speech, it can be "u" before the letters ב,ו,מ,פ and before the shva vowel: ושתיים ushtayim.
Is the Hebrew "or" inclusive, exclusive, or both depending on context?
I mean, could this sentence end in an answer of, "both are happy," or is it setting up a situation where only one of the two could be happy?
Same as English, only one word for "or".
Are there languages with different words for inclusive and exclusive "or"?
I don't know, I was just trying to think of a situation where this phrase would be uttered (as a learning technique) and was curious if it was possible for it to go either way.
I just don't want to learn something wrong, thinking it could be inclusive when it couldn't be. :)
And Arabic! "Aw" is inclusive in Standard Arabic, while "Am" is exclusive.