While sitting in a square with an object token while stealthed, can your opponent destroy the Object out from under you? I would think that they would need a clear line of sight to the object but wouldnt be able to, due to the character in stealth. Please tell me if I am wrong.

They can blow up the object you are standing on. The figure on it does not block fire to the object.

However, when the object is destroyed, it is replaced with a rubble token. So your figure is still in hindering terrain.

But at the end of the turn, the rubble is removed is it not?

Only if something tells you to remove it. Honestly, I can't really think of anything that does tell you to remove normal rubble.

I think you may be thinking of the rubble generated when a Barrier is destroyed... that rubble goes away when the Barrier tokens go away.

That must have been it. I think a judge may have told me at one time that a destroyed objects rubble was removed at the end of the turn, that's the way I have been playing it. I guess I won't be from now on

I always enjoy having a superstrength character pull the object out from under the stealth opponent so the rangers can shoot them. Even better if the superstrength guy has charge and uses the object first!

I had Hulkbuster run up to Agent Brand and yank the object out from underneath her, then Hulkbuster went into soaring so that Gambit could running shot up on her. It was an awesome move that worked perfectly! My opponent never saw it coming.

This trick only works if you have some way to ignore opposing characters during movement though - such as flight, Leap/Climb, Phasing/Teleport, Hypersonic Speed, Transporter or the Movethrough or Sneak feats. If the Super Strength figure does not have a way to ignore opposing characters when moving then it must stop immediately upon becoming adjacent to the enemy, before it has a chance to pick up the object.

I have another question regarding object tokens. Before the match starts, is it optional for either person to not place any objects on the battle field? Can they be taken off of the map? Can they refuse so that only My 3 be played? And Do I still have to take turns with my opponent placing the object tokens if they decide to not play 3?

No, you don't have a choice in playing three objects. Unless a BFC says otherwise, you need to put out objects.

So you must play them on the map. Thank you, just had an issue earlier today that kind of bothered me regarding objects.

If you don't want to play objects for one reason or another, you can always place them in the far corners of the map (where they are unlikely to do anyone any good) or place them right in front of your starting area and destroy them on your first turn (which is especially easy if you play a Sentinel or other Colossal... just walk over them).