I'll answer your questions as best as I can.
I live in the state of California. Most of the cons that I attend are held in Los Angeles and there is a con Every 1-3 months. Usually con will last for 3 days. ALA is going to be held for 3 days. If you count Day 0, then it is 4 days long.
How many times a year are they held? Each con is held once a year; but there is a con almost every month, so there is plenty of variety.
So how your cons are held? I don't quite understand this one. I mean, they shouldn't be any different than any other convention. Just more people. Celebrities from the USA(and sometimes from Japan) are known to be invited to these conventions.
Are there many people and are there any competitions, if yes which? There are lots of people. The smallest con I went to had 200 people. The largest one I attended, Anime Expo, had nearly 50,000 people! There are always competitions. Masquerades and Trading card game battles are the only ones that come to my mind right now.
AC Paradise: Cosplay Photographer
The Mighty Darknut from the Legend of Zelda series -- November 2013 - present
Sagi from Baten Kaitos: Origins -- Anime Expo 2014
Marno from Baten Kaitos: Origins -- Wondercon 2014
Rorschach from The Watchmen -- June 2012-January 2014/Anime LA Exclusive
Fulgore from Killer Instinct -- Indefinite suspension