Here's a link to the rules that you might find useful: http://www.homepokertourney.com/robe...m#THE_SHOWDOWN
1. Yep, first to act shows first if there was no betting action on the river.
2. You can muck. Anyone else who was in the hand is entitled to ask to see your cards though.
3. Dunno that it's unethical, but it's definitely not classy. I think it's the not turning your hand over bit that bugs me the most - especially if you have the nuts then just show your cards. It won't have any impact whatsoever on your right to see your opponent's hand: if you're OK with being "that guy" then you can still insist in seeing his cards regardless.
4. Showdown order is you (last aggressor), then the other player in the side pot, then the all in player.
5. Not sure I understand what you're asking here... but I suspect the answer depends very much on what type of game it is and where you're playing it.
If it's a tournament then the answer should pretty much always be "no" - in a tournament, the cards are supposed to be flipped up before you even finish running out the board.
In a cash game it's possible something like that might be allowed, depending on house rules etc. There was a hand between David Benyamine and Guy Laliberte years ago on High Stakes Poker that probably fit this description, where they got all in, then decided on a chop arrangement without going to showdown, or even finishing running out the board. I can't remember whether they showed their cards or not in that situation.
If the hand does
go to showdown though (as in, all the betting is finished and the full board has been dealt) then the rule is that anyone who wants to claim any part of the pot has to show both of their cards (see rule 1 of the link above).
6. No, they can't (again, see rule 1 in the link) and yes, you're absolutely within your rights to insist on seeing both. Especially if you're in a casino though, you shouldn't have to. The dealer should do the insisting for you, and not give the player any part of the pot until all of their cards are shown.