Say I want to play a rogue with oracle as my subclass- does the character get bonus spells via the Mystery class feature? If I do, how many times per day can I cast the spells? Or is it assumed the character doesn't get any because it lacks a spell list?
No bonus spells. Bonus spells is its own class feature.
You get only what it says you get, so you don't get those mystery spells anyway (nor patron, nor bloodline, etc).