RM1610 is good for X and Y since the higher pitch means you can get a higher feedrate with limited critical speed, however since the Z-axis screw is so short there's no need to do this, so stick with RM1605 on Z to maintain good resolution.

I advise using bigger rails on X and Z. Particularly Z since the forces on Z are a similar magnitude to Y, so you shouldn't use smaller rails.

For a 1:2 ratio you don't want 10:16 pulleys for two reasons - for a start 16/10 is 1.6 not 2, and also it's not good to have such small pulleys as you will have less teeth engaged in the belt which can lead to premature wear and possibly reduced accuracy. It's best to use at least 15T, so 15:30 would be good. Also HTD pulleys are better than XL.

The BK and BF mounts both hold bearings, the difference is the type and quantity. BK has two angular contact bearings inside, which means it can resist both radial and axial loads, whereas BF just has one 'standard' bearing in it, so only supports the ballscrew radially. If I were you, since you have the lathe, I'd make my own bearing mounts from aluminium. It's not that complicated and you'll be able to do a much better (and cheaper) job of it than the ones from China. They are often too tight a fit, or the seal rubs on the nut or other annoying thins to correct. I've never bought the BK/BF blocks myself, but I know people who have and they've all needed tweaking.

Also making your own ballnut mounts is a good plan simply because it's so much cheaper. Here's one I made earlier:
Click image for larger version. 

Name:	ballnutmounts (Medium).jpg 
Views:	1552 
Size:	77.1 KB 
ID:	7353