1. The red "C" does indeed mean that there are combat reports for you to read.
1.a. The combat reports in question can be found (by default) by pressing r on the main screen. It then gives a list of creatures that have done battle recently, and you can select them to see a detailed overview of the battle they were involved in. It isn't perfect, and isn't quite as detailed as what is in adventure mode (the most glaring omission is that it fails to list most fatalities), but is still pretty cool.
2. There is currently no known way to seperate bones, shells, skulls, and raw hides (which is what the tanner needs) from otherwise-useless body parts like hair, nervous tissue, and various severed limbs. This is something that most everyone sees as a problem, especially given that there was a way to do so in the previous version. All of those things are now simply found in the blanket "body parts" section of the custom refuse options.
3. Set up a refuse pile that accepts only corpses and your haulers will drag corpses to it. If there's an unrotten corpse from a butcherable creature near your butcher's shop, the shop will automatically quene a butcher animal job, and your butcher (who you should turn off all other labors for if at all possible) will handle it.
Unfortuantely, there is not currently any known way of seperating rotten corpses out from unrotten, butcherable ones, and it is very annoying to make the refuse stockpile automatically seperate out butcherable and non-butcherable creature types. This, unlike the body parts stockpiles, was also not an option in the previous versions, so it isn't quite as annoying to veteran players.