edsotherhalf

You are required by law to carry your green card on you at all times, so your wallet is the best place for it if you like to follow the law.
Obtaining an I-551 stamp in your passport through an Infopass is going to be the best way to be able to travel internationally. New Infopass slots open daily, so you should continue to check (I see some very early appointments in the next couple of days at my local office, for example), but you may well have left it too late.

I just renewed my passport and got it back two weeks ago. I added my married name to the passport. I had to fill out the long form. The renewal form is only if everything on the passport is the same. You have to do the full form for change of name. I was told it would take 3 weeks to receive it back but got it about 10 days later. Hope this helps.