I have no fucking clue how to engage a 'hook-up' at Uni not at clubs.

Club being a nightspot? Join a club or two (ie an extracurricular group of like-minded people). You'll meet people that way, and even if you don't, they are fun and was one of the best parts of my college experience.

When the fuck do I ask for her number assuming we just met/spoke?

"Hey, it was fun talking with you. Would you want to [get lunch/grab a drink/snort some lines and fuck our brains out] some time?"

Is 'we should watch a movie at my place' and 'we should have coffee at my place' really mean 'let's have sex?'

Well, invitation to hook up at least, but don't assume you will be having sex (but do be prepared if you do! Have a condom! Or two).

I fine it extremely weird and uncomfortable if I talk to a stranger. I mean the only way to make friends is talking to them right? I have no clue how to engage in convos both for male and female.

Me too. You gotta power through it, and push your comfort zone. Some people you won't be able to no matter what, but some times it just clicks (platonically or romantically). Be confident. Like I said, joining a club can be a great way to meet people, and doing so also gives you an automatic in to talk about something you know you'll both find interesting.

How do I go clubbing alone -_-'. Most of my friends are indoor gamers but I want to go to clubs but not alone because my friends hate clubbing and those drinking events. Is it weird going out alone? There's a social clubbing event my Uni hosted I don't know if I want to go alone.

I never enjoyed clubbing, and pretty much stopped after my freshman year. Not all its cracked up to be. Also a major money drain!

How do I flirt? I heard that 'talking' and 'being nice' is flirting. It just makes no sense to me because if I want to talk to a chick but I don't fancy her that means I'm flirting she might get the wrong idea I'm trying to hit on her but truthfully I'm not meaning to.

Be confident. Not ass-holish 'player' confident, but be confident.

And lastly, is the only way to become 'wealthy' to own a successful business (I know it's extremely hard not that naive) because I'm in University studying Commerce law and I feel like I'm going to get piss paid, not enough for my satisfaction and to afford my dream car. So basically, is College worth it and being an employee worth it?

Are you planning on being a lawyer? Cause that can be a pretty well paying gig.