Admittingly, the setup, with potential downloads and the organization of transitions in the transition room are currently not optimal. The search option will help and bit. Let’s hope that in the next release this will improve.
Some of the standard transitions you mention are in the transitions room under General: The Fade you mention when applied between two clips fades the first out and the second in. But notice that when you select the transition in the timeline, above the timeline a "modify" button appears. Clicking on that will enable you to change some of the behavior of the transition, including cross or overlap, and (depending on the transition) whether it goes up or down, right or left. If you put the transition at the start or the end of a clip, without letting it overlap the adjacent clip, it will fade in, out etc. without showing the adjacent clip but (mostly) black instead.
I also cannot find a plain diagonal transition. There are some that look like page turning or sliding diagonally, but that is likely not what you are looking for?
The previously available 3rd party software (Adorage) that could help you out, is not there anymore.
There might be some (but not too many) transitions in the various creative packs that can be downloaded and you can also try to find the transition you need via the Free Templates button that directs you to the Director zone.