At what age does a puppy go on heat for the first time? Also can being around an unfixed male that is trying to mount (we separated them after he tried and FAILED), cause the puppy to go in heat early?

Around 6 months give or take a little time is when they usually go in. Being around a dog that wants to mount won't usually speed the process up but if he is wanting to mount then more than likely she is getting close to coming in. Unless she is way young and then his mounting could just be a way of him telling her where she ranks in the pack according to him. If she is close of age you will need to watch like a hawk, never leave them alone together, and possibly get diapers to put on the female to save your house from the blood and it can also serve as a bit of a barrier to protect her from the male. Once she is out of heat, usually in 3 weeks, then you can get her fixed. You could go ahead and get the male fixed now, if he's yours, but males can still be fertile for a few months after the procedure so you won't be saved the headache this time around even if you do get him fixed now.

She's almost 3 months old and the other dog isn't ours, it's my father in laws Shih Tzu that was causing the problem. Needless to say I was extremely mad that I wasn't told he wasn't fixed before going over there. We're more then likely getting our husky fixed soon.

First heat cycles can happen anywhere from as early as 5 months to as late as 18 months.  No, mounting and humping cannot cause an early estrous.  Humping/mounting is not entirely sexual, though it's a good idea to separate like you did.  Young puppies can often contract UTIs and Vaginitis that may make them smell more enticing to a male even not being fertile.

Thanks. This is my first female dof, so I don't know a whole lot yet