In Rip Disc>Options>CD,DVD,BD>File Management make sure "rip to a single file with cue..." is unchecked
make sure that under CD Ripping all the drive names have copy mode:secure
then RIP Disc>Options>Encoding, choose your Encoder (i.e. FLAC, APE, whatever)
this is my setup and it rips to single FLAC files and auto creates a log file (secure rip). i don't generally make .cue files unless i want them for some reason
there is NO difference between ASIO and WASAPI as far as sound quality, they are both bit-perfect streams. sometimes one will work better than the other with your external equipment (DAC) but that isn't something i can answer
in general, WASAPI will be easier to use but if you have it working good with ASIO, there is no reason to change over. The driver setting will not affect Rip settings