can it be correct to say:
I have lived here since 2 months ago.
I haven't seen them since 3 weeks ago.
I mean can we use 'since' with 'ago' in this way? Or is it totally wrong?
I have lived here for two months.
I have lived here since 16th November.
I moved here two months ago.
I haven't seen them since the end of December.
I haven't seen them since December 27th.
I haven't seen them for three weeks.
It sounds odd to me the way you have written them, but I wouldn't completely disallow "since" with "ago" when there is more information.
I've been losing weight steadily since two months ago -- questionable.
I've been losing weight steadily since I started exercising two months ago -- perfectly fine
She's been despondent since four days ago -- questionable
She's been despondent since her boyfriend left on a business trip four days ago -- perfectly fine
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.