>My questions are:
1. Should I be able to see these on my bees? I went through every hive yesterday, saw drone larve with no mites and couldn't find any bees that appeared to have mites on their backs.
If you have trained your eye to spot them, possibly. Most people don't see them.http://www.bushfarms.com/images/Varroa2.jpghttp://www.bushfarms.com/beespests.htm#varroa
>2. How will I be able to tell if my hives start struggling with mites?
You need a count. A natural drop on a sticky board or a board under a SBB in 24 hours (or more than one day divided by the number of days) will give you an idea. A sugar roll can also be helpful. You need to quantify them.
>3. Is splitting a good way to break the brood cycle and interrupt the mite cycle?
A walk away split would break the brood cycle in one half of the split.http://www.bushfarms.com/beessplits.htm#walkaway
>4. When would these have shown up? I never saw evidence of them in any of the past 3 years of beekeeping. I didn't see any evidence last fall, but they're getting cleaned out of the hives this spring.
They died and are being hauled out with the trash. You have had them the past 3 years.