What is the name of the menu on the right of the map (containing locations, quests, etc) and
Is there a way to resize it ?
(I want it to go less low so i can add something in the bottom right corner)
Use an addon like merTorchbug or Zgoo and move your mouse above it, type in /tbugm or /zgoo mouse (or use the keybinds) and youz will inspect the control below the mouse.
These "menus" at the right are often re-used menus, not only used at the map. So changing it might also change it elsewhere (see Perfect Pixel info below).
I think you can have a look at the addon PerfectPixel how it alters he map controls there. But I think the left and right "menus" are some standard ESO backdrop controls which are just "replaced in general" by PP, so that they will (and only are able to) change in total for all menus.
But if you ask me: Changing these menus height etc. will just make you break many other addons