Well I suppose these answers have to be half opinion, but I do have some manuals here to reference for fun.
1. Maybe. I would say yes, unless you're in the mood to be nice. The Draconomicon says the gizzard is lined with bony plates that grind up food, etc. It also says it's charged with elemental energy, something I mention below. If everyone assumes the DR is from the Scales, maybe these plates provide said DR in the gizzard.
2. Yes, (Draconicon) the feat 'snatch and swallow' (not sure how much I can say legally, but I'll give my opinion on what it says)
It appears that any damage a swallowed character deals is take off your hitpoints.
it also appears an escape artist check would allow you to crawl back into their mouth, basically escape the stomach.
it also leads me to beleive that a chart shows damage to cut your way out, but that the muscles close that hole back up, if someone else was to be swallowed, they'd have to do it again.
3. No, But it's your world. Some of these dragons it shows the breath weapon being like poison sacks on a snake, and in the mouth only; however, in the anatomy section it says that the dragons fundamentum charges it's lungs with power for the dragon's breath weapon. If you check the SRD on Snatch feat though..
http://www.d20srd.org/srd/monsterFeats.htm#snatchIt states that a snatched creature held in the mouth does not get a relfex save vs. breath weapon.
According to the Draconicon manual a character in the stomach takes bludgeoning damage each round, AND energy damage each round. The type of energy is based on the dragon's breath weapon.
4. Why not. If you don't want to just make it easy, give the dragon itself a Fort. check to cough up the character. If you want to be mean, let him puke up enough acid (stomach juice) to still cause some damage.
According to the Draconicon manual a character in the stomach takes bludgeoning damage each round, AND energy damage each round. The type of energy is based on the dragon's breath weapon.
I assume I haven't gotten any legal feathers ruffled since I haven't listed stats or numbers, just discussed idea's and overall rules.
Now if you take into account the amount of bite damage you take while snatched up in a dragon's mouth, and the fact that you can't dodge a breath weapon, I don't really see jumping into a dragon's mouth on purpose. Who says he has to swallow you before you're dead. The SRD link also reminds me that it's pretty much a free bite while sntached, and that you can drop a creature while you're flying. So again, why swallow, Bite, Fly, Breath, Drop them for falling damage. Kill off one, and let the others realize they don't want to play in the gizzard park afterall.
If you're group is to powerful, or determined to grapple their way inside a dragon, then maybe the DR should count. I don't see anything here that specifically states it, but I don't see anything that doesn't. That being said, when it doesn't specific an exemption, I usually stick to the basics, which would mean the DR stays.
Unless you have nut-ball rule lawyers, I'd just run it as your world, just once you decide, try to stick with it. If they're getting overrun by the dragon, and you're doing the eating for flavor, I'd leave out the DR, so they can escape, but if they start trying to dive into his mouth on purpose, I might remind them by letting someone get chewed a round or two, and breathed on, before being swallowed. You could always restrict str bonuses and such, do to restricted movement. Can you really get all your strength in if you're not able to swing at something, or get your footing?
I think the problem is deciding if you're trying to be nice, or if you're worried your group is going to overrun a dragon, or go on dragon killing sprees.
Then it might be time to find a way to make them captured and naked.

After reviewing this info, it reminds me why we were suppose to be afraid of dragons in campaigns.
Well i've rambled enough. I hope this helps in some form.
(sorry if it seems over rambled, I was getting phone calls [work] and interruptions. I tried to clean it up some)
There are decent examples in the stat blocks of some monsters in the MM also, with more exact numbers and explainations.