Difficult to see detail because images are slightly out of focus.

As for the small black bumps on the bark -- do they easily lift off? If so, they are scale.

That would explain the stickiness as some kinds of scale excrete honeydew.

I'm unable to determine what you're referring to as the "white fuzzy" stuff on the leaves.

Yes, you have scale - two different kinds to be exact. The white fuzzy stuff is cottony maple scale; the dark spots on the trunk/branches is gloomy scale. Both can be rather debilitating insect problems that are difficult to control. And the sticky stuff is their excretion, commonly known as honeydew.

A horticultural oil applied during the dormant season can be effective in eliminating/reducing overwintering populations but your situation looks a bit acute for that delayed approach. I'd take samples and these photos into your local extension service for more specific treatments and appropriate timing. With scale, timing of the treatments is critical.