That's quite a mouthful, so I'll try and address questions one by one but you can always ask for more info later on...
- Would there be a difference if you actually had a degree, one that has nothing to do with game design at all ?
That entirely depends on the field you'd be looking to get a job into. Artists preferably have one, programmers absolutely do need, designers come from every walk of life. That's a generalization but you're likely to encounter that. Obviously mod work can replace a degree, even more favorably if the mod is widely known and presents some groundbreaking stuff. Day of Defeat is one example of a mod that didn't require degrees from the team for them to get hired. Given you have no experience in modding beyond several years ago, it's very likely you can't count on that.
I would say, absolutely stay with the degree if only to secure yourself one, which will help you in your life regardless of whether or not you can enter the gaming industry.
- Well, can you still get a job without any degree but a strong portfolio?
Yes you can, again preferably in design and art departments. However you do need that strong portfolio (most of the time) so you better get to that.
- Should I drop out and try my luck, or still try get my degree even though it has nothing to do with game design and I hate it with a passion ?
Hating your degree is a luxury I'm really not sure you're in the position to afford. That sounds rough, and it is, but I think more than anything you need to finish that degree, if only to prove to your future employers you can finish what you start. A degree is a start, however irrelevant to the position it may seem at first. A degree doesn't only teach you skills, it gives you a method to working and delivering on what you were tasked to do.
- Say I do drop out and get a job, is my lacking degree preventing me from moving up?
In my experience, I really don't think it will. You'll move up based on your achievements and the games you work on, not because of your degree. A degree is a gateway into a career, you make your own luck after that.
- What are my chances of getting employed in North America as a EU citizen nowadays?
Without any prior experience, absolutely none nowadays. To get a work visa in the US, your employer needs to prove that your addition to the team brings something no US citizen could do himself/herself but first and foremost you need to have a degree. Period.
Things aren't so tough in Canada, where for instance you don't need a degree (relevant to your job or not) but companies won't give you a chance unless you've started proving you can deliver. Again Day of Defeat was good enough for one other Mapcorian to try his luck here straight from Europe, so you get the idea of how big your work needs to be before that's the case. And this was 5 years ago.
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I've seen some nice job offers, say I apply for them(based in CA/US) and they want me for an interview do I get a refund for my flight/trip?
If a company wants to see you for an interview, they will provide all the necessary accommodations and pay for it. WHEN you get to that stage in your career, you probably already have worked on some title.
- Or how should I start? Is it "cocky" to apply for jobs overseas when you have no work experience at all?
Cocky or not, you most likely will never hear back from them. If you really are going to work in this field, you need to start by giving yourself the chance studios won't give you at this stage. Pick modding up again, do your own designs, and prove you're someone that can bring something valuable to the existing team.
I would also advise you to stay in Europe for now. For one thing the paperwork will be inexistent to get you a job. You can find some good studios in Germany that can get you a foot in the door. I've seen guys in the modding scene getting interviews recently, there is demand for entry level positions still. Hell it only took me one map before Ubisoft took me on, so you could be that lucky (as luck really plays its major part too)