Good questions. As for AIing a beef cow on pasture we just get them into the corral with a bucket of range cubes. Have to have gentle cows for this but then again why would you want to AI a crazy cow.
IDing calves in pasture, now that can get tricky. Lot depends on the cow. Several methods work.
1. Wait until they are a month or two old, separate the cows and calves overnight, eartag the calf, let it out, see who it sucks. Write down the tag number in the cow's records.
2. If you just have to tag it as a newborn you can roll a hay ring out to where the calf is, drop it over the calf, crawl in the ring, tag quickly and hope the cow doesn't try to come in the ring with you.
3. Have someone ride in the back of the pickup, swoop in between the calf and cow, grab it and jump in the back of the truck, tag it. Get some distance between you and the cow and set the calf back down.