A green card holder can sponsor their spouse for residency from inside or outside the US. The difference is that outside the US, it involves filing form I-130 with USCIS and visiting the embassy/consulate for interviews, while inside the US requires filing two forms: I-130 and I-485 with USCIS.

Yes, they can and they'd have via consular processing through a U.S. embassy or consulate, as opposed to adjusting status if they were within the U.S.

Mistake with my earlier comment. Sorry. What I meant was:

Yes, they can and they'd have to do it via consular processing through a U.S. embassy or consulate, as opposed to adjusting status if they were within the U.S.