Obliques and abdominal exercises. The best way to really isolate those areas would be a dip station (basically just a kind of chair looking thing that puts your legs off the ground and uses your upper body to keep you there [by your forearms or else on the handles] so you can do leg raises and twists and that sort of thing - really, really isolates the obliques and abs if you do it right). Failing an actual dip station, there's the two parallel bars on playgrounds (actually, even school lunch line areas) that can serve similar purpose (wear rubber gloves though, for grip). I can say from personal experience, it is WAY better than doing those on the floor. Since I don't have access to either myself, I've been using the < junction of the kitchen counters and its effective enough (don't do that unless you know the counters can handle it. Some can't).
But then there's also the Russian Twist/Landmine 180's with a barbell (or even a weighted medicine ball+decline bench thing with the leg anchors). Apparently that's even better and I can see why, given the instructional videos. I plan to make that my go-to as it gets both the obliques and abs at the same time. I don't necessarily have wide hips (they're about the same as my rib cage) but I am still overweight, especially in my core, so they might as well be... but yeah, those will certainly help if bulked up to offset larger hips.
Unfortunately, no. That's just what E does. That won't regress or stop happening excepting a dangerously, very low BF%. Or until T and some work. In the interim, I also vote the underworks slimmer/compression shorts (or the longer binders that basically do the same thing).
And actually, in my experience, if T itself induces fat loss (it certainly has and continues to for me), that will actually help to shift the weight and not just the distribution. But yes, it takes some work too in order to really get it to get off of that particular area (e.g. T makes the fat in the offending appendages reduce and puts it elsewhere so yes, T can and does do that and not just there).