Diablo IV - A Return To Darkness

I made it to level 40 and got my horse. My first action of course was to run around exposing as much as the map as I could. So much fun! I just suck at playing video games, so I’ve died lots of times with my cold rogue. Death penalties are basically nothing though (hardcore excepted of course).

Questions:

When you go into later difficulties, do the codex rewards for dungeons change? I’d love to clear out every dungeon, but some of the rewards seem pretty weak, and if they are different later, I’d just focus on finishing the last two acts.

Do you keep your horse ability when you start a new character?

Do blue exclamations give you any unique rewards that you couldn’t get otherwise, outside of renown? I’d be inclined to skip them all, but not if they are required for a special codex or skillpoint, etc?

Edit: Also the use of Obols. I’ve turned them in at the curiosity vendor trying to get a good bow. Three times in a row he has given me a simple bow. Am I doing something wrong, or is it just a teeny chance of getting something decent?

Thanks