I am new to HeroClix and have never entered a Tourny.
Can you have more than one of a character on a team?
Such as 3 Doombot's or 2 Vulture's?

yup, its considered cheesy and in some venues they do disallow dupes, but according to the standard rules its ok.

however only one unique or limited edition of a certain figure can be fielded.

if youre going to use dupes, keep it to support figs and taxis to prevent the cheese flag from being flown overhead.

or not, hey if it works it works.

you can make any team you like except that in official sanctioned venues you will restricted to making Marvel only or DC only games. You can make teams of dupes all you like as long as you do not duplicte a unique or LE with the same name on it's base. For instance if you were going to make a team with Spiderman on it in duplicate you could have Rookie Experienced and Veteran Spidey all on the same team but if you wanted to add Uniques you'd have to choose either the Black suit Spidey from IC or the Six Armed Spidey from CT or the Web Shield Spidey from Xplosion but you could not have more then one Unique Spidey on the team. I hope that was clear.

As far as cheesy is concerned .... everybody has thier own opinion with only a few universal agreement like using multiple Firelords or Firelord in general. Some people feel duplicate generics are perfectly fine. I myself love using Doombots. I also dont mind using multiple Harlequinns when playing DC. If you are playing the game to win do what you have to do. Some people want to keep the game as close to the book as possible.

In that case just remind them of the worst comic story of all time Maximum Clonage. Seriously. Just have fun and don't let people's house rules affect your team building unless you are playing in a tournament with established rules that say no duping.