First off we all get these sort of times in life. Be assured whilst there are times you are down, it doesn't stay that way. You'll be on a high again in time.
Sure, whatever is wrong it is important. Don't beat yourself up for feeling low just because someone somewhere is worse off. It is always the case that someone somewhere is worse off. Doesn't take away your right to feel the way you do.
If you have broken up with someone it is usually a good idea to give them a wide berth until the new situation has been accepted. Pulls too many heart strings otherwise.
There are all sorts of friends. The one you mention isn't giving yo what you need at the moment, that's unfortunate but you ought not hold it against him. Unsure what you were looking for from him but maybe you need to look elsewhere ?
Your parent's rows are their problem. Yes it's difficult to cope with, but again don't beat yourself up about it. They're old enough to sort their own relationship problems out. It's not your job. DOn;t let them use you to talk to each other, they are old enough to know that isn't fair. Tell them so in case they missed it.
Good for you for trying to protect your sister from it all, but you can not work miracles. Feel good for what you do achieve not bad for not having a magic solution.
I reckon dad can buy his own tickets to somewhere. Tell him isn't not fair to drag you into his and your mum's disagreements. The more you let them get you involved the more you will be blamed unfairly.
Again don't go overboard. your sister probably knows something is wrong, you can't hide the world from her, but it's nice you minimise the affects. But keep it in perspective, you can't spend everything you have on the issue which is your parent's responsibility anyway.
Note how some of the things you do with good intent is what is making things hard for you. Find a balance that is less depressing and stressful.
If your mum decides to move out, and it is no forgone conclusion that she will, it will be her decision. Don't create extra stress on yourself worrying about what might be and yet may not be after all. Take things as it comes, and again, be aware that nothing ever stays the same. You may be down now but for sure there will be times ahead when you've come through it a better person.