Yes everything plus those three functions. I tried the older remote early on when I found that the 397 didn’t have those keys. I don’t use it regularly as I’m still using the 1888H recorder in another room.
All you’ll get will be x2 and x4, that’s all the machine allows.
The only recording problem I’ve had is using RW discs (freezing, break-up, etc.). This is probably the fault of the discs themselves, and doesn’t occur very often. I’ve recorded again on the same discs and their fine. I use Verbatum and Philips RW discs.
As I said I’ve transferred SP VHS to hard drive and disc. It’s recorded digitally, so the original quality does not alter. The same applies to LP recordings. As long as you record in SP mode it should be OK.
The 397D is the only “name” brand I’ve seen at those prices. Aldi sell their brand recorder now and again, but I don’t know anything about them.