Heifer replacements I'll train them to drink off a feeder and they get whole milk and surplus colostrum till weaning at about ten weeks. Bulls and any heifers I don't want for replacements get picked up off farm between four days and 2 weeks old as 'bobbies'.
I've occasionally put a few calves on a nurse cow - usually a cow who is lame or otherwise unfit to stay with the herd. Sometimes it works well and sometimes it can become a nightmare - I had an old high SCC cow last year that would only let the calves feed if she was hobbled, even though she'd been a nurse cow as a three year old.
I don't even know what a butt pan is. If the cows are calm they don't make too much mess. If they do, it gets hosed off asap and I'll spray the walls with chlorine about once a month to remove any that's dried on... and try not to take clear photos when it's needing done. Seen some sheds that are just spotless but my priorities lie elsewhere - those guys are physically wiping down the rails and walls every milking. Or their cows just don't poop.