Multiple alternating Time Signatures

1) you're stuck unfortunately
2) you have some options if you select the time signature then go to time signature properties (use button in Inspector) and enter alternate text. I don't think there would be a way to show C, but you could enter 4+7+4+5/4+8+4+8, for example. Or you could use the Symbols palette (press "Z" to display) to construct this manually, which might look more exactly lie you want but would be more of a PITA and I'd worry the manual adjustments required to get it to look exactly that way might be "fragile" and not look the same in future versions of MuseScore.

Actually, although I say you're stuck on the first point, there are creative solutions, including starting your score by importing an ABC file that is set up that way. Go to Plugins / Plugin Manager and be sure the ABC Import is enabled (it has a habit of disabling itself even if you enabled it previously). Then run it from the Plugins menu and paste the following in:

X:1
M:none
K:none
[M:C] z8 | [M:7/8] z4 z2 z1 | [M:C] z8 | [M:5/8] z3 z2 |
[M:C] z8 | [M:7/8] z4 z2 z1 | [M:C] z8 | [M:5/8] z3 z2 |
[M:C] z8 | [M:7/8] z4 z2 z1 | [M:C] z8 | [M:5/8] z3 z2 |
[M:C] z8 | [M:7/8] z4 z2 z1 | [M:C] z8 | [M:5/8] z3 z2 |

This creates four copies of that sequences; just copy/paste that last line as many times as desired to create more.