Either they are nice and my type and I am aroused around them but they have a boyfriend or married with kids, or they are not my type, single and fat, or pretty but very stuck up and rude.
Ah, very common pattern, it's easy to make generalisations about what might be true for your own country or region based on your prior experiences, if your prior experiences haven't gone as you would have hoped. This is common for many guys. The one thing I would add is, when guys do meet a girl that they're attracted to, it's incredibly common to care too much what she thinks, too muchn for what's necessary. Sometimes this can sabotage interactions. Even if most girls you have met have been taken, either that's just unforuntate, or only the one's that were taken you've been paying the most attention; I'll focus on that in later paragraphs. If that has been your experience, it's very easy to make broad, sweeping genaralisations about your own are, region, entire country.
I think that a large part of your problem is reading-into any positive interactions that girls might give you as a sign that this might be 'the one' which of course, adds excess pressure, causes you to care too much whether you fuck-up, makes it difficuolt to 'be yourself' and otherwise hiners you. Sometimes this can make you're interactions with girls you feel that way with go south.
I have cold approached many girls in public. I have approached girls in class. I lost weight. I did everything, but still, no girl wanted me and until today, I feel no girl wants me. This leads to why I am depressed.
Mate, that's the wrong approach to go about a problem like this. Too much focus on results. At best, this way of meeting girls, or trying to dispel the idea that 'I'm undatable' through external validation won't help. Many of us would argue that search for external validation is setting yourself up for failure, or riding on a pale horse. I can't comment on your exact situation, I don't know the specifics, or what you find difficult in the situations in which you're meeting girls under. Trying to proove 'Im' likable to girls I find hot' through this means is NOT the way forward. It's probably best to meet girls through meet-up groups, or through things you're interested in (I know the old, boring, trite cliche). Seriously, when you meet girls in situaitions where you're not 'looking', it'll occur to you that 'yes, I can actually talk to girls'.
The 'all girls having boyfriends' bit, might be where happier abroad might help and signpost you in the right direction. As far as shortage of available girls is concerned, yes, you may well find that as you expand your horizons. Most likely by coincidence or your own spins, or as most would argue here, there is genuinely a shortage of availabe, attractive girls. But as far as what I'm talking about is concerned, I think the old 'look at oneself first' bit might have a huge amount of value. It will only serve you well in future, abroad or at home. That isn't to suggest that you're inadequate socially, or have a bad personality, or are undateable in any way, but just the thought patterns and beliefs, and possibly reading too much into potential prospects, causing too much pressure, making it difficult to 'be yourself' could be the root of many of your problems.
You say you have aspergers. Join the club. I was diagnosed at a young age. I've seen how that's hindered me and am only sharing the sense. Social andxiety and putting a negative spin on everything and making that an excuse has been a major hindrance to me and is the reason why I ask you to consider what I've said. I'm not suggesting that has been to you but, I'm happy to help if you need it.