The black spots look like some kind of fungus. This is why we don't spray the leaves with water (Unless we have to) and why we spray during the dormant season.

You may be able to keep this from spreading by spraying two tablespoons of wettable sulfur per gallon of water. Spray the whole tree and all the leaves top and bottom.

In the future spray with Bordeaux fungicide once when they are dormant and once just before bud break.

Molds and Fungus grow on the tree during the dormant season. They grow on the buds that become leaves too. Spraying Bordeaux fungicide twice as directed will kill the molds and fungus that cause leaves to turn black and die off. It also kills the stuff that causes Peach Leaf Curl. A dormant oil spray can kill/suffocate all the nasty insect eggs that are waiting to hatch on your trees too.

The white stuff looks like Woolly Apple Aphid's. Do a google image search to get a good look see to make sure.

Here's a link you may find useful...
http://www.ca.uky.edu/entomology/entfacts/ef219.asp

If you have major infestations during the summer and want something totally safe to spray you can always use 2-4 Tablespoons of Dr. Bronner Peppermint Castile Soap per gallon of water. It can also be used as a wetting agent for insecticides. Just add one Tablespoon per gallon to your insecticide and shake well. In fact I bet this would kill your Woolly Aphids if you mixed it at 3-4 Tablespoons per gallon of water and sprayed it on them.

Thanks, Thisisme. I'll give the sulfur a try. I don't think the white stuff is Woolly Apple Aphids, it doesn't look like the images I Googled.

I'm thinking mealybugs. I had two sages that became magnets for these nasty little bugs. Sadly, by the time I noticed something was wrong, my two plants were dead and dying. I lost them both. If you think that's what you have, I'd read up on control methods. It seems they also cause black mold so your two problems may be related.

This is the best IPM site that I've come across. http://www.ipm.ucdavis.edu/PMG/r107300511.html#MANAGEMENT

Here is a link that might be useful: mealybugs

It can be hard to see what they are unless you look closely with magnifying glass. There are lots of different stages in the life cycle of Woolly Apple Aphid's. They look different in each one. Even the size of an infestation can make them look different if you aren't looking really close.