Slopes
The only mount available right now is the Scorpee, which has a longer hitbox than the player. As such, it may think it's jumping when you go up hills. Ideally, on hills, you'll wanna have the creature adhere to the slope its on; in other words, give it slope physics.
Mount Combat
Currently, it's impossible to get hit by monsters or hit monsters when on a mount. For this, I'd say keep the stats the way they currently are: based on the monster's own stats. For combat, I would recommend mobs target the mount instead of the player while they're on the mount. Players already do that, so why not?
For the mount itself, I would give it its own HP bar, which will appear below the money counter. It would have a green color on it and have a fixed size just like the EXP bar.
Healing Mounts
For mounts, I would suggest they have their own set of consumables. This is primarily done in order to show that mounts are like pets. As such, I would suggest mounts be separated into three categories: herbivores, carnivores, and omnivores. Here's what I got:

The carrot already exists in the game; it's asset sits in the Farmer's Market sign in the game. And yes, I'd like a carrot to be put in the game. In any case, these are all based on things that you would feed animals.
I believe wild mounts are meant to be temporary, so to fit this, there would be a "hunger meter"; the larger the creature, the more it takes to get them full. This would also be fixed size just like the suggested Mount HP bar and the EXP bar in players. This time, the bar would be colored brown.
I would think the larger the consumable itself is, the more it would fill a mount, so yeah. There's that. And yes, the mount-exclusive hunger meter is an anti-exploit mechanic.