I'm not sure if I follow all of your post, but if I do, your assumptions are correct.
A 2C1R can be as small as 14cM or as large as 353cM on Ancestry. A 3C may not show up as a match.
With 3X great-grandparents (4th cousins if on the same generational level), there is around a 50% chance you will match with 4th cousins.
If you have a 2nd cousin match, the shared matches for them might contain 3rd cousins, 4th cousins, some 5th cousins and maybe some more distantly related ones. As you mention it depends on the DNA inherited. Sometimes you will get those overlaps, which can make things very easy to triangulate marriages from shared matches.
As an example, I have one cluster of matches for a Humphreys family, where the matches are 5th cousins, then I have two other clusters of matches for the family, where the matches are 7th cousins.
The reason will be that my test subject has inherited something like 35cM from a pair of 4X great-grandparents. The cluster of 5th cousin matches could match with 21cM of that; while the two separate clusters of 7th cousin matches will match on DNA from that same 35cM, but no more than 7cM of what the 5th cousins have.
There are likely other Humphreys descendants who have tested that have DNA other than the 35cM my test subject has. Since the total cM of a person is about 3400cM, 35cM is just about 1%.
This is why it's useful to get tests from other relatives, like 1st, 2nd, 3rd, 4th cousins; and even siblings. I have about 10 tests from descendants of 3X great-grandparents. Let's say from one aunt's test there is 330cM inherited from the 3XGGPs. If you add in the other 9 tests, maybe that goes up to more like 2,000cM. We can't tell as Ancestry doesn't have a chromosome browser. So with about 2,000cM of the ancestors' DNA, you will not just have a few more matches, you will have multiples of more matches. In this case I think it's probably 5-10 times more matches.
You can match with quite distant relatives, at least as far back as 8th cousins. It just depends on if you and another relative happen to have inherited the same small segment of DNA from an ancestor. And when you do match with 8th cousins, they will rarely overlap with more recent clusters of 7th, 6th, 5th, 4th etc cousins, because the chance of having the same segment of DNA as an 8th cousin is less than 1%.