1. I think I'm correct here but hopefully Eric will chime in if not. Anyway, IF the data is rendered and in a known color space, I think that's sent to the print module. So if you have a TIFF in Adobe RGB (1998), there are no further LR parametric edits applied, I suspect Adobe RGB (1998) not Linear ProPhoto is sent to the print module. IF the data is raw or has LR adjustments, then I'm pretty darn sure Linear ProPhoto is used to process the data. Then that is sent to the print module.
2. I believe that's a function of the print driver or maybe OS, I suspect sRGB. It is probably possible to find out exactly by getting hold of the print data. At least on the Mac, you can turn off the driver, print and examine the PDF spool file OutputIntent profile.