Yep. If they ban drag performance, and don't recognize trans identity as valid, then trans people presenting as their gender would be considered "in drag." Merely going out in public would be criminalized, which is the point. They want extermination, but will take disappearance in the meantime.
Yes and no. Obviously, trans and drag are two different things, but they are hated for the same reason: transgressing gender normativity and especially showing it's OK for AMAB persons to have and display characteristics traditionally assigned to femininity.
So yes, equating trans with drag is wrong for all reasons, but this doesn't make this cartoon transphobic, only realistic.
Indeed, one need not listen to TERFs and conservatives for very long to see that they happily conflate the two as "men in dresses." (FtM people simply don't exist unless it's someone they liked to jerk off to pre-transition)