Maybe 2 doesn't make sense and the examples you provided would be more natural, but 1 is definitely correct, I think. 1 appears in a grammar book's exercise example. Maybe they made an error, but in this sentence it is "one of my friends" that connects to the verb "loves", not "I".
1. One of my friends as well as I loves her.
You mean this doesn't makes sense, either? If so, maybe this is only a grammatical sentence.
*He as well as I loves Bon Jovi.
The only way you could make that even remotely acceptable
would be to use commas or brackets:
He, as well as I, loves Bon Jovi.
He (as well as I) loves Bon Jovi.
That way, at least it's clear that "loves" belongs to "He" and not to "I". However, please please please
bear in mind that just because a sentence can be constructed, that doesn't mean that it should be, or that a native speaker would ever use it. I cannot imagine any circumstance whatsoever where I would use any construction other than the ones that were clearly given to you by Barb.
He and I love Bon Jovi.
He and I both love Bon Jovi.
He loves Bon Jovi and so do I.
I love Bon Jovi and so does he.
I love Bon Jovi and so does one of my friends.