It's easy in the sense that it's more or less a sure thing. It's not easy in the sense that you still have to go through a lot of paperwork and bureaucracy, and even have to go in for a doctor to poke you and prod you to see if you're fit to live in the US. Nothing like being treated like livestock to make you feel welcome.
It was way easier for me to deal with the Italian bureaucracy once we were married than it would be for my wife to go to the US. And that's saying something: Italian bureaucracy is about as bad as the stereotypes make it out to be.
The Fed Govt. doesn't recognize same-sex spouses (e.g. if you're married in Canada, South Africa, etc.). This is due to DOMA. There is currently legislation under way to try change this (UAFA).
Many other countries do recognize foreign same-sex marriages for immigration purposes, even if they themselves don't recognize same-sex marriage.
Married spouses at least (other spouses aren't accepted) but you're assuming the parent had a visa himself (well assuming the parent is male as lesbian couples aren't recognised either) and that the particular visa he had was one of the visas that grant a spouse rights.
Yeah I think you're typically right. I guess I interchange partner with spouse in my mind because of the whole recognition of de facto couples here in Australia and the whole civil union bit.