Is Tournament Chess different from regular Chess?

At my school, I play chess often.

Yet, everytime I play the 'rules' are different. For example, I was playing this girl and right about to queen my pawn but she said, "You can only do that if your Queen is dead." but another time, one guy got 3 queens.

She said that she played in a tournament and that was the rules.

Honestly, I'm just confused about Promotion in Chess. If a pawn is promoted, can you immediatly kill it (if you have the means to)? Or is it against the rules too?

When I was playing said girl, she didn't kill my queen when I queened a pawn but another boy killed mine when I queened it.

And, can you randomly change the rank of a promoted pawn?

Yes, there's a clock and the dreaded touch move rule. 

That girl was just making up her own rules, real chess you can promote how many times you want. 

I'm no  expert but I believe that yes, you can immediately kill (capture?) a queened pawn.