In the coming months, more and more consulates will be switching to the e-visa system and we can assume by sometime next year, that's all there will be left.
No, immigration won't transfer visa stickers obtained at consulates abroad. They'll turn you away and tell you to travel with both the old and new passport.
You present both passports. Immigration won't transfer visas. They will only transfer extensions of stay, obtained in country and you would do that through your assigned immigration office only.
If your passport expires with a valid DTV in it, you carry the old passport along with the new passport whenever you enter and exit Thailand.
I've done that before with a non-O multiple entry visa. The only time I got my visa (actually extension of stay) transferred was when I had an in country non-O 1 year extension, which was then transferred to my new passport. That took up 3 pages in my passport! They copied all the previous extensions as well.
This is the DTV group, not the general visa group. Nevertheless, for the time being, there's a 60 day visa exemption, which may revert back to 30 days at some point in the future. I don't think the 60 day visa exemption is being planned to be permanent. It will probably stay in place for the remainder of the high season but could go back to 30 days sometime next year.