Turn 21 in a month, and I finish university in about a year. I still live with my family because I don't have the time to work enough hours to afford an apartment, and get the grades that I do. I still work though, but my parents help with certain bills until I graduate. My recommendation is if your parents are willing to help you pay for things without it taking too much from your life, accept the offer. In your case you will be building your life while you are away, so to have some of the financial burden shouldered while you find your feet is really important. Taking on every single responsibility that comes with being on your own will crush you. Don't get discouraged because you rely on your parents for things. You've realized now that you need to make moves on your own, so begin taking the steps to do it. Don't think about what was; think about now, and tomorrow.

I'm not sure ultimately how stuff works outside of the US in terms of up-bringing, but personal finance like Elisza said is of great importance. Keep track of what your spending, and for the love of all that is good learn to save. You have no idea how many friends I have that spend money on going out, concerts, etc. then complain about being broke. I'm not saying you can't do fun things because you can, just learn to control yourself. Sometimes it isn't worth it. Having a good line of credit is always a plus and makes life easier in the future. I read the bit you said about part-time jobs, and to be honest the money isn't great. I have a two job currently that I juggle with school. I think the point of having those jobs is just learning how to juggle your affairs. I still get through school with a grade average that is much higher than the class standard, and get my work done. They teach discipline, but that is a personal experience.

Finally, the social skills thing is pretty simple, but it is harsh. I myself try to do it because my social skills lack the finesse that I notice in others. Try to start up a conversation with anyone. The only way you are going to learn to be a conversationalist is to actually talk with people. It may go shitty for a while, but as you pick up on the basic cues you will get better. When I say start up a conversation with anyone I mean anyone. Age? Doesn't matter Gender? Doesn't matter. Style? Doesn't matter. That is probably the best advice I can give you to begin building this skill because it is really all that matters.