Happy to jump in on answering these too
1. Yes she is, and it helps prove the point that drag can be interpreted/expressed in any number of ways. I'd say the core definition of "drag" is performance through either a different gender than your own or an embellished/over-the-top version of what/who you are. The conventional definition is "female impersonation," which is generally true but you've seen on the show how some queens aren't really gunning for looking "female." Either way, since Derrick's drag fits that definition she's absolutely a drag queen. Celebrity impersonation is impressive to me but yeah, she interprets her style through such a tunnel vision that I don't find that inspiring.
It's fun to see different people use drag differently. Think of someone like Willam, Bianca or even RuPaul, who don't really change personalities when they get in drag but just use it to elevate the visual. Their demeanor relatively stays the same, and by doing drag they're essentially matching their real personalities with a preferred gender. Versus a BenDelacreme or Sharon Needles, who not only transform their look but their personality as well. They're character queens, which is a personal favorite of mine because it's much more focused on performance.
2. Drag queens tend to perform in nightclubs and gay bars, the traditional performance style is through lip syncing, which is why the bottom two each week have to lip sync for their lives. Some perform live, some do interpretive performances that don't fall under those categories, but generally the crowd holds out cash for the queens to walk by and collect mid-performance. If you remember in Season 6 Darienne Lake did an impression of taking money from a crowd during her second lip sync, it's the traditional thing. Drag and lip syncing have gone hand in hand for decades now, though as you've seen on the show not all queens excel in that style. The interesting thing about the drag scene now is that most queens think that the only way to make a drag career truly lucrative is to get on Drag Race, which is sadly true because there are now 100 alums who are more likely to get a club booking than a local up-n-comer. That's the caveat of having a show like this be such a phenomenon; queens all over the country are hungry to get on the show just to validate doing drag in the first place.