Why don’t some keys like C-. work on xterm?

If your xterm version is 216 or newer, you should have keys like C-. and C-, if you add the following resource specification to your ~/.Xdefaults:

 XTerm.VT100.modifyOtherKeys: 1

If you want to use uxterm, also add the following:

 UXTerm.VT100.modifyOtherKeys: 1