If there is a latency difference between ASIO and WDM, it's because the vendor did a better job with one or the other. Neither is inherently faster/slower. So if ASIO seems more efficient, then go with that. Sound quality will be identical regardless of which driver you choose.
The drivers are active all the time, even when you're not actually using them. The reason zero-latency monitoring works without newly-recorded data getting out of sync with previously-recorded data is that SONAR knows how much latency there is and compensates for it automatically. The recorded audio isn't just dropped in wherever SONAR hears it, but rather where the audio
should fall after taking latency into account.
If you're getting 6ms round-trip latency, that's actually quite good. But you have to measure
total latency, both going in and playing back (hence the term "round-trip"). The only way to measure that accurately is with a loopback, where you run a cable from one of your interface's outputs back into one of its inputs. This isn't usually worth the hassle unless you're troubleshooting a timing problem wherein SONAR is not applying the correct amount of latency compensation. Most of the time, you can judge by ear whether the RTL is small enough or not.