D standard would be ok, a bit too tight for me. C# standard I think would be the best. Then C standard I think it would probably start to get a little floppy, but just barely. But that's my opinion. A lot of people I know play C standard with 10's, and to them it just feels right. It's just your opinion really.
They'll do. I tune to D standard on my electric sometimes and I use 11s. It could probably do C# but it would start getting floppy. C... well if you don't like tight strings you'll love 11s in C. I prefer higher gauges at higher tensions, so I would find C standard too floppy. As mentioned above though, some people would find that perfect or maybe even a little tight.
Those strings would be great for C-standard, even though Not even slinky would be a bit tighter
Brigadier of the 7-string legion. 7>6

Fender Telecaster
Schecter Damien 7
Engl Fireball