No, you cannot stamp your own passport. It must be done by an official authority.
Stamp act
Yes, you can request the immigration officer to stamp your passport.
No, I have never had any issues with a deported stamp on my passport.
Yes, did you get a stamp in your passport when you left the US?
Have you ever gotten a stamp in your passport from Canada when you traveled there?
Have you ever gotten a stamp in your passport from Croatia when you traveled there?
"Have you ever gotten a stamp in your passport from Jordan when you traveled there?"
"Have you ever gotten a stamp in your passport from Romania when you traveled there?"
"Have you ever gotten a stamp in your passport from Serbia when you traveled there?"
"Have you ever gotten a stamp in your passport from Sweden when you traveled there?"
"Have you ever gotten a stamp in your passport from Taiwan when you traveled there?"
"Have you ever gotten a stamp in your passport from Uruguay when you traveled there?"