That's a good question. Eye contact is pretty crucial to me because it's a clear sign of flirting between two individuals. Yes, maintaining contact does establish dominance.
Remember how as children, some of us would have staring contests with another person to see who could last the longest? The first person to blink would be the loser and be considered "inferior" to the winner. However, TOO much eye contact will start to creep some people out. That's why whenever I hold eye contact with someone, as soon as they look away, I look away too. Then when they look back at me, I look back too.
Telegraphing interest while maintaining eye contact is simple. Flash a genuine smile here and there and you're golden. I don't think everything is "lost" if you look away from a girl. Everything is lost if you don't have the guts to look at her again!
As for establishing dominance over other men, I used to have that problem too. When I was working on eye contact with other people, I had difficulty looking at other men in the eyes. But as time passed and the more I did it, I realize how incredibly easy it was and now most men I pass by look away before I do. Here's a little cheat I used to do when I was having trouble, maybe it'll help you.
Instead of looking in the other person's eyes, look at the spot in between their eyes! It makes you look like you're staring that person down

They'll be looking away in no time after you do that for a good minute or so haha.