What about if they put themselves in a position where their hand would be auto-mucked such as after a clock countdown or them abandoning their hand and getting up to take a phone call (but not until action is on them)?

TDA rules don't allow a player to fold in any of these situations. They'd face either a warning or penalty, up to the tourney director's discretion in each instance.

Heads up if you both have chips you can simply muck. It's not a good idea and may raise some flags to anyone looking for collusion, but I've never seen anyone get in trouble for it.

In a multi-way pot you are not allowed to fold unless you're facing a bet. Abandoning your hand (for a call or bathroom break) does not excuse it. Doing so will rarely get you a penalty but it can happen especially if you're a repeat offender.

It affects how the hand plays out and gives information to those after you that was not available to those before.

If you run out a clock when not facing a bet, you are forced to check not fold.

Never seen 'clock' called on a guy tanking a check/bet spot, but I guess there was a lot of scuttle at the last two WSOP MEs with tanking PF and WKassuf's banter when making decisions, which I assume some were when not facing a bet. So I would think that it's a forced check, not fold, if it were to ever happen.

This WSOP has gone really well I think, but there was a 15 minute tank/call that occurred .. thankfully the guy was right and won the pot!

There are a few threads about 'open' mucking in turn as well. However, it's REALLY frowned upon in the tournament setting.

It's basically the same thing that PHell is being taken to task about when he went into a rant in a three-way pot when he action wasn't on him. It allowed the player that action was on know that he wasn't strong and allowed him to call and eliminate a player since it was 'more than pretty sure' that PHell was going to fold. GL

What should happen with the cards that are pushed forward when a player attempts to fold his hand when he has the option to check? Should they be mucked or given back to the player?

If I were dealing I would just leave the cards where they end up until action returned to that Player, provided they didn't interfere with the Board or any other Player's cards. When action returned to that Player I would ask "Is that a Fold?" and then swipe into the muck pile.

If my instructions as a Dealer are to call the Floor in these spots I would do so, but still leave them untouched. If the Floor is not 'required' to be called, and none of the other Players at the table ask for the Floor, then I would warn the Player after the hand about the rule and it's possible repercussions. GL

Muck them and warn the player not to do that.

They is places that hand out 2 hand penalties for folding or acting out of turn during their tournaments. So its not too out of the ordinary if you ask me

He wins the pot and the other players are mad at you.

or

He loses the pot and he's mad at you.

Yep