i don't think he went to the princess just to get revenge on Guts, it's not like Guts show any personnel affection towards Griffith that it'd hurt him by doing so.
he went to the princess because he lost an important chess piece that can do all the dirty work for him, he probably still has alot of enemies to kill off, and sleeping with the princess was also part of the plan to get secret support from her, just that he decided to execute the plan out of shock & not doing enough planning. But to think he can't win the royal guards without his sword means that he probably won't be able to with his sword. He'd probably knows what'd happen to him and probably knows there is this torturer down the dungeon, but he just gives himself up. I guess this is the only way to set the storyline up.
Guts probably didn't like to get it from behind from experience.
I dunno ... Guts and Griffith have a super complicated relationship. Very odd. After Guts beat him, he broke down and I suppose his leave left him numb (empty, broken even), but really not feeling anything; so I guess he slept with the princess to feel something (and according to that montage, all he could see was Guts' face while doing the deed); this also explains why he easily submitted to his arrest and torture. He just didn't give a damn. I mean, he already had the affections of the princess, and plus he was making his way to the top so there was no real reason to lay her.