Ctrl+M sends the same character(RET) as the Enter key in terminal. Programs have no way to tell them apart, so these keys cannot be configured separately.
Ctrl+Q is already used for XON by default, so it cannot be used by Bash, but you should still be able to use it in tmux, because tmux uses raw input mode.
A GUI program could read from the keyboard, that Key m has been pressed with modifier Ctrl and use Ctrl+m as a shortcut, but a shell or any terminal program recieves the Ctrl+Key combinations just as ascii characters from 0 to 26
Ctrl+@ = 0
Ctrl+A = 1
Ctrl+B = 2
and so on. You can try this to see the values
cat ctrlkeys <<EOF
od -c ctrlkeys
0000000 001 002 003 004 005 006 \n
To enter the values press Ctrl+v before Ctrl+[a-f] to get them uninterpreted as a raw value.
When you look at the ascii(7) table you can see the control codes in a table with the corresponding characters @..Z on the left. For example
015 13 0D CR '\r' (carriage ret) 115 77 4D M
011 9 09 HT '\t' (horizontal tab) 111 73 49 I
The next layer that interprets control codes before bash is stty (change and print the terminal settings)
intr = ^C; quit = ^\; erase = ^?; kill = ^U; eof = ^D; eol = <undef>; eol2 = <undef>; swtch = <undef>; start = ^Q; stop = ^S; susp = ^Z; rprnt = ^R; werase = ^W; lnext = ^V; flush = ^O;
see stty(1) for the meanings of
Also see readline(3) as bash and other GNU cli programs use that library to control input lines and of course bash(1) /READLINE, the readline section of the bash manual page.
Note: XYZ(NUM) means manual page XYZ from section NUM, so the result of
man NUM XYZ.