How to achieve C-q like behaviour of c-electric-paren

C-q is quoted-insert. It inserts the next character literally¹. This cancels any special behavior that is configured for the character (by binding a command to the character, as well as a few other mechanisms such as abbrevs). For example, ( in C mode is bound to c-electric-paren, which is what triggers special behaviors such as potentially inserting a matching parenthesis and reindenting the current line. Pressing C-q ( just inserts a parenthesis because that's what C-q does: it ignores any key binding for (.

C-q C-m inserts a literal control-M character. Emacs prints C-m as RET when describing key sequences. Unfortunately, for historical reasons, there are two control characters associated with line breaks: carriage return = control-M, and line feed = control-J. This dates back to typewriters where a line break required two mechanical operations: returning the carriage to the left margin, and advancing the paper by one line. On keyboards, the Return or Enter or ⏎ key sends the control-M character. But in text files, on most modern platforms except Windows, a line break is represented by a control-J character. On Windows, a line break is the two-character sequence control-M control-J, but Emacs converts it to control-J internally²2. As a consequence, C-q RET doesn't insert a line break, it inserts a rarely-used control character. To insert a line break with no special effects, you need C-q C-j.

There is a separate mechanism by which you can pass a numerical argument to the next command in a generic way: prefix arguments. If you press C-u, then type some digits, it passes that number as the prefix argument to the next command. For example, C-u 4 2 ( invokes the command that is bound to ( (so c-electric-paren in C mode) with the prefix argument 42. There are a few other ways to type a prefix argument, including M-4 M-2 ( and ESC 4 2 (. (ESC alone doesn't start a prefix argument, only when it's followed by a digit.) This prefix argument is what interactive functions get when they use p or P in an interactive specification. p is the numerical value, while P gives you more control, in particular to distinguish between no prefix argument (nil) and an explicit argument with the value 1 (1).

For insertions and motion, there is a convention that the prefix argument N means repeating the command N times, and also bypasses “electric” behavior. For example, M-1 ( inserts a parenthesis with no electric behavior, because c-electric-paren detects the prefix argument and does not perform any electric behavior in that case. Similarly, M-1 RET or C-u 1 RET inserts a line break without triggering some of the usual extra behaviors. However, the default newline command still performs some extra things even with a prefix argument, such as indenting the newly created line.

You can choose what to do in your advanced-return function based on the prefix argument. Use P in the interactive specification and only invoke special behaviors if the argument is non-nil ((when arg …)).

¹ _{Except digits, which let you insert a character via its code point, but that's not relevant here.}
² _{Similar to how C converts line breaks to a single '\n' when reading text files.}