Ox carts will go to one direction and back.
For example, Vernworth has 2 ox cart "stops". One ox cart will take you to Melve and back. The other will take you to Checkpoint Rest Town and back.
You don't control their destination.
I've only had 1, on occasion maybe 2 fights while on an ox cart. Most weren't anything to write home about. Some goblins.
I've only had 1 encounter while camping. I usually clear out the are before making camp.
I realize that now. I guess it seemed like I had some control over it because my destinations were between the same 2 towns for quite a while. Most of the encounters for me are the goblins or wolves, but I've been attacked by the ogre several times as well.