So, is what you mean something like:
tap "x" = delete context-sensitive
hold "x" = delete menu appears
?

In that case I think it may be less frustrating if we just kept to a key that toggles between select all/deselect all (the "A" key), for now.

@Bartosz Moniewski (monio) makes a very good point! If pressing outside the mesh deselects all, then when the manipulator is in grabing position it should pop out more, or change color, so that we can distinguish whether it's going to grab the manipulator or deselect all. The same with vertices. In maya if you hover over a vertex it changes color, to tell you that if you press LMB it will select that vertex.

@michael knubben (michaelknubben) I also prefer your second solution. There could be some sort area very near the tabs where if you scaled down the panel to that small area, instead of showing ridiculously small buttons, it would snap to only the tabs (and then if you carried on scaling it would eventually snap to callapsed tabs and panel, as it does at the moment).

@michael knubben (michaelknubben) It's very good! I only think that one should have the option to collapse the panel completely as well (including the tabs).

@Campbell Barton (campbellbarton) I just realized how arrogant I sounded in my previous post. Sorry. Didn't mean it that way. Changing the GPU did work. Thanks.
Is there a reason you can think of why it doesn't work with this specific Graphics card? Would it be fixable?

@Warren Bahler (russcript) I know it's logical, just not practical, in my view, that when you press "draw" on the toolbar you have to open the properties panel on the other side to change the color and thickness. Maybe this could appear temporarily in the bottom part of the toolbar when the grease pencil is created, as happens with some addons. I don't really have the solution.

@Warren Bahler (russcript) I also get lost in the properties panel much more than in the toolbar. Besides that, I think it's got properties that could be seen as tools.

Oh. Sorry.
Thanks.

Sorry. I didn't see how uploading a file would help, since it happens in every file I use, in the installed version and on the zipped version of Blender. But I'll upload one.

@Marco G (marcog) @Bartosz Moniewski (monio) @William Reynish (billrey)
The mockup made by @Paweł Łyczkowski (plyczkowski) is pretty good (see above, in one of the comments by @Warren Bahler (russcript) ). The divisions are pretty clear. I prefer the arrow in a light grey than in a darker grey, because I think it's important that it's easy to see if it is an expandable menu button or not.

@Archie Call (acall) You do make a good point, but I don't think it works better with stacked text. I thought it maybe would, but it doesn't. Also, I realized this week that Maya (which I have to use for work), has vertical tabs with rotated text and I had never questioned it. So, although your effort is perfectly understandable and appreciated, personally, I don't think it would work better.

@Archie Call (acall) I was thinking just that (stacked vertical text). Definitely easier to read. However, with your mock up It looks uglier to me. Don't know if it's just the font you chose, though.

Hey.
I've been working on a proposal for the keymap revamp for the last week. I've had experience in a few 3D packages, and I currently teach 3D animation at a University in Portugal, so I thought I could try and help. Hope it helps:

@William Reynish (billrey) I don't think that would work well, since for rotation, for example, double tap "R" makes it rotate in Trackball mode. In my opinion, it doesn't apply well to G, R and S.