Before you get your knickers in a twist, do your homework and take a look at this:
Every single issue you have mentioned has been answered in the wiki. For those that aren't, there's always the University of Google:
It can be really useful in these cases if you mention the size of the file in question. That's not necessary for now, but if you try the solutions mentioned in the wiki and have difficulties, please let us know what you tried, how you tried it, and what the results were, including error messages.
You've leveled up, so now there's an entirely new skillset to acquire. Fewer limits does not necessarily mean fewer problems, just different problems. If anything, I have found that being on a VPS means you have to be even more knowledgeable about how a web server works, but the benefit is that you can do things that shared hosting would never allow you to do. There are always tradeoffs.