Go for it! I'm an English teacher.
The "of" you're talking about is a shortened form of "have", as has already been pointed out. It's usually pronounced "uv".
If you use the modal verbs "must, might, may, could and can't" to talk about past probability, they are all followed by "have" which is usually contracted to "uv".
Say the following without contracting the "have";
I was in love 100%
I must have been in love 95%
I might have been in love 50%
I could have been in love 50%
I may have been in love 50%
I can't have been in love 95% not
I wasn't in love
You see?
As for "gotten" that isn't British English. It's the past participle of get in American English.
The verb get is one of the most used verbs in English and I bet you couldn't go a whole day without saying it. I could give you a list of it's uses but it'd be exceedingly tedious, so I won't.
