If I understand it right : When my character is making an opposed check like Stealth(my character) vs Observasion(my opponent) I am the only one forming and rolling a dice pool with my opponent only adding some misfortune and challenge dice in my pool.My opponent will not make a roll.If I roll at least one success I pass the check.

On the other hand,when making a competitive check each PC and/or NPC involved in the forms and rolls his own dice pool.Right?

yep.

Yes.

Plus, a competative check often uses a track, either using a tug-of-war style or a straight "race" track, while opposed checks can use a track, but (IMO anyway) don't normally warrant one of their own.