Thank you for your reply Tom 
Window menu (at the top) > Right Zone
Then click on the icons and the options should appear. Leave it open if you wish.
re memorizing: no one does this, it would be a little like memorizing a dictionary before learning to converse with anyone.
As you practice with Dorico, you end up memorizing, but that’s what paper and pencil could be used for, right?
(Otherwise you could use Zotero or similar, your students may be doing something like this for their research, learning anyway? I mention it here.)
Popovers for example are laid out quite logically (mostly) like tempo things being in the Shift-M (for meter). As you get used to it, sometimes you can simply type something in you have never done before and it will appear (like 13/8 is entered in the same way as 3/4) (sorry for an obvious example!)
In the bottom zone, you will see different options, like accidental, hide note, scale … and Engrave has other options (sometimes the same for convenience).
As @benwiggy mentioned, there would be too many to have in a contextual menu, look at the right zone for other options, but combined, bottom and right zone have the majority of what you might need?
Dorico has a different way to accommodate all this as you have found.
If you have time (trying to finish a project with a very limited time factor is unlikely to be the way to do this), you will get used to the key commands and options, but unfortunately it does take time to learn and muscle memory. We have all gone through this and most of us have adapted and find input in Dorico in a clear easy way.
For the ASAP, best to use Sibelius? learn Dorico when you have some research time instead?
(You can export xml in Dorico to Sibelius if you need to.)
Under pressure, with complete frustration, you probably won’t be learning much Dorico otherwise (and probably not fair for your brain either.)
(I sympathize, I am currently working in Musescore, trying to input and feel totally hopeless … you know, it isn’t Dorico (or Sibelius which I came from, nor Finale which I have used.)