It's been my understanding that using a mix of 3/32 and 1/8 components was harmless (provided of course it's a 1/8 chain), but w/e. It's more likely that your loose chain tension is caused by something like not tightening your nuts enough, but someone with experience with mixed drivetrains can chime in on that.

You can use the same lockring, that has nothing to do with cog size.

As for 48x17 vs. 48x15, that one's really up to you, but keep in mind that those are two really different ratios. If you find the 48x16 steep at times then going to 48x15 won't be a good idea, and likewise if you find yourself spun out at your current gear the 17t won't be your best bet, although the former scenario is much more likely. Since you mentioned skid patches, it'll be much harder to skid with a 15t cog than with a 17t.

Gear ratio is one of those things that you should really select based on riding conditions and personal preference, not skid patches. If you don't want to change it, your best bet for getting more skid patches would be to go for a 47 or 49 tooth chainring, though that will be more expensive. Again, the 47t will make your ratio slightly lower (but not as much as changing a cog) so I'd err on that side for skidding purposes.