Switching to mirrorless.. Nikon or Sony?

[unpopular]

Will IQ drop if I attach an adaptor to take other lenses with different mount?

That's going to depend on the individual lens characteristics. Older lenses with less contrast and a tendency to flare will perform with less apparent IQ than modern lenses. Some like the "softer" look and go after older "legacy" lenses. One thing to look out for is attempting to adapt Canon EF lenses to bodies that cannot electronically control the aperture. Micro Four Thirds bodies especially.

Well, yes and no. These are more qualities of the older lenses than the adapter. So long as the adapter doesn't have internal correcting lenses (i.e. speed boosting or SLR adaptors for shorter register) then there is no perceivable reason why adapted lenses would perform worse.

Some rangefinder lenses with significant retrofocus may behave oddly however due to that the sensor cannot detect light as easily at a severe angle.