That doesn't mean he's marbling. He's just becoming less stressed. That's usual when bettas first get a new home. Imagine being shipped in a tiny bag and forced into a cup. You'd probably be stressed, but as soon as you found an owner and got space (in this case 10 whole gallons) you'd brighten up and become happy.
Side note, when you get your cories AFTER you cycle, make sure you take Buddy out and move around the plants and cave then put the cories in and then Buddy. It will make sure Buddy doesn't try to defend "his" territory since everything has been moved around. So he'll be less likely to attack them.
If you adapt them properly to a change in pH, then yes they will be fine in your water.