Skills are handled "old-school", which means there isn't a formal "skill system" or "list" as you have in a typical d20 system or a classless RPG. What a class can do is a matter of reason & logic and Judge/Player discretion. Is it reasonable that all adventurers should be able to Run/Jump/Sneak? Probably. Is it reasonable that all adventurers can slay dragons, be kings and conquerors? Yes, if they're high enough level.
So deciding to use a d20 or a d10 is up for you group to decide. Whatever your group decides, write it down to be consistent. DCC RPG is flexible enough to expand create new rules for particular things that you group finds important. I personally use variable DCs, that step up or down depending on difficulty and skill. But a group could easily use a more granular system, by using the Dice-Chain instead. For example, climbing a cliff. A thief can roll a d20, a fighter can roll a d16, a cleric and wizard should probably roll a d10 or d12. On the same check versus the same DC.
Mounted combat seems also a bit confusing.
To avoid falling from a horse you roll a D10... against what?
When in doubt, it's usually a DC 15. But in this case it's DC 10, page 87. You may have read it wrong.
If you are trained because of your occupation you get a +2?
Doesn't your dice change to a d20?
Yeah, I'd say it's a typo. A hold over from when the skill check rules were being refined. Pick the one that makes the most sense to you and your group, and stick with it. I use +/-2 mods mostly out of habit, but I'm trying to get into the habit of bumping up or down the dice chain.
