I'm pretty sure I made several positional errors in this game, but I don't know how I should have played better. Please help by pointing out mistakes as well as better move alternatives!

Your worst strategical mistake is your attitude after 10. dxe5. Yes, your Bishop is closed and you have some problems with b7, but White King is weak and his pieces are not developed yet. 

So, after 17. ... Nxd4 your chances would be not bad.For example 18. Nxd4 Qxd4 19. Bc3 and even 19. ... Qc4 with plan  ... b4, Qb5, c4 if he would not attack your Queen with 20. Qe2 or something else.

But at some point you lose this game in your head, so there was no chance for you to recover.

Interesting suggestions, thank you.

During the opening, would 6. ...e5 have been better? Also, was ...Bg4 a good idea?

Sorry, i'm not interested much in Opening - I would surely play 6. ...e5, but that's not the point. Your lack of determination is the worst. You should play till your King's sore death, if you have some sort of counter - that way you will gain skills even if you'll lose. But you seem to care a little about that, and i'm not interested in Opening, so have a nice day.