Wash-up? That's what paper towels or tissues are for -- to wipe out the pot and dishes. If you cook so the food cakes on to the pot, then you're not doing so well. I've spent days bush camping by bike and used minimal water for wash-up.
Frying? If you reconstitute jerky, or use other packaged/tinned meat products, they generally have already been cooked. It's not impossible to keep fresh meat fresh, largely by freezing it and wrapping it in clothing and stuff, but generally it's got to be used by the second day, so preserved or dehydrated meats are a better choice.
I like TVP (textured vegetable protein) in granular form as a non-meat protein. It is light-as to carry, reconstitutes quickly with water, can be flavoured with just about anything, and has the final texture of minced meat. And because it is dehydrated soya bean, it won't go off in the heat, and can be served up to a vegetarian if s/he runs short of food.
The Thermos idea is a good one and is not new, but you have to be prepared to carry around an extra kitchen item -- the flask -- as well as something to heat water. Is it an efficient means of cooking, or not? In terms of fuel usage, maybe; in terms of extra bulk on the bike, maybe not.
I'd much rather carry a can of aerosol cream instead, and make up several batches of pancakes to spray the contents over... I cook the pancakes on the Trangia frying pan, and they can be either for savoury mains with something like an instant pasta inside, or dessert spread with jam, honey or maple syrup. The pre-mixed commercial pancake packs are pretty good, although it's best to pay a little more for the better quality.
I can't go touring for long without fresh vegetables in a typical stew format. I like to have a thickened stew, so taking along a small amount of cornflour is a good idea. The rice idea also is a good one, although I prefer to prepare mine separately. I usually do take two Trangia pots with me, and use the absorption method to cook rice -- bring water and rice to boil with lid on, when boiling, take off heat with lid on, and leave for 15 minutes or so.
And as Machka said, it is entirely possible to tour without the need to cook. But beware canned foods -- you are likely carrying water for no real purpose other than to throw it away.