I helped the king in rags this time, but now I can't enter the keep because the jarl and guards attack me and throw me back in jail. If you help the king, are you not able to stay in the reach after that? Bought a home there
Nope. But you can incur a bounty by fighting post-escape.
The "bounty" you get for "killing" the people pre-Cidna mine isn't real, in game terms. It's just something NPCs say so you can get stuck in the mine. Afterwards, it's explained that the Jarl himself cleared you of the "crime" you "comitted." However, if you fought the guards after you get out, you WILL get a bounty.