"Comma" or "and"?
Case 1:
In §2.1 and §2.2 we prove ...
or
In §2.1, §2.2 we prove ...
Case 2:
As mentioned in Section 2 (§2.1 and §2.2) ...
or
As mentioned in Section 2 (§2.1, §2.2) ...
"Comma" or "and"?
Case 1:
In §2.1 and §2.2 we prove ...
or
In §2.1, §2.2 we prove ...
Case 2:
As mentioned in Section 2 (§2.1 and §2.2) ...
or
As mentioned in Section 2 (§2.1, §2.2) ...
Replacing “and” with a comma is “Headlinese”, where normal rules of grammar are superseded by the need for brevity. You should not do this in prose like your case 1.
However, I do like parenthetical comments or references to be brief, so I might use this technique in your case 2.