Yes, definitely remove spider webbing. Some of them contain small or large spiders. The white stuff many be a fungus. Don't feed leaves that have fungus to caterpillars. Water from the bottom, not the top if possible. Also, wash and dry the milkweed that you are feeding your caterpillars--that will help gets some of the small insects off.
I'm having to do the same thing in my yard. Squishing, washing off, squishing.... I used Ladybugs before the Monarchs came. I don't recommend ladybugs when the Monarchs are laying. Ladybugs will eat Monarch eggs, too.http://www.mymonarchguide.com/2007/08/m ... blems.html
Milkweed leaf 'problems'