My female RES occasionally lays infertile eggs in the water. She usually eats them, but I'm not encouraging any breeding with them, so I'm sorry I can't help
Yes, but mine always laid in the water. It's all about having the right conditions. Nesting box needs to be large enough, deep enough, the right temp and consistency. The lighting and ambient temps might come in to play. Water conditions leading up to the oviposition.....
I could never figure out why I couldn't get my females to lay in the nest box. Those eggs were always eaten by the time I got to them..
I know Mitchell Cowles keeps many adult RES Morphs indoors for a large chunk of the year, in Medium Waterlands and he has bred them successfully.
The morph part really doesn't matter too much though. At the end of the day, they're Trachemys scripta. It surely can be done and has been probably 1000 times, I'm sure.