Carrier bearing is the bearing that supports the driveshaft as you thought. What goes wrong with them is they wear out and get loose and noisy.
No idea what the thrust spindle is , have them point it out. Could be a clutch thing, or , a front end part or, who knows. Maybe it is a Ranger specific part I haven;t heard of. Sounds like gobbledygook mechanick speak to get more $$. Not that I am cynical.

U joints are checked for play or binding. Best checked if the driveshaft is removed so you can inspect it and the tranny and rear end are not holding it. But you can usually do a good enough job putting the rear end up on stands, placing the tranny in nuetral, and tring to detect play as you rotate it or push forward or back. Check the carrier the same way, it is mounted in rubber. I kinda doubt BOTH a u joint and the carrier failed simultaneously. Especially on your truck, which is in great shape.
Front shafts are checked the same way.