If you could hear your brake pads rub from bike flexing, have your spoke tension checked to see if your spokes are all a bit loose. I think all bike shops have a spoke tension meter, but many mechanics in the shop might not know how to use it, someone that knows wheels would have to check it.

Descending on hills, if you start to feel any wobble or shimmy, put one or maybe both knees against the top tube of the frame, that can absorb some of the shimmy and bring things under control. You might want to try a few descents with one or two knees pressed against the top tube to practice it first so that the leg position becomes something you are familiar with.

One of my bikes has a very slight shimmy when it is fully loaded at about 27 km. I find if I loosen my grip on the handlebars, it goes away. This is counter intuitive, you would think a tighter grip would be a sensible solution, but in my case too tight a grip makes it worse.