I'm trying to figure out if I can lay down wood in my 1960 house. There are three areas that I'd like to cover with one cohesive flooring.

I don't think we can remove all of the flooring in a cost effective way since there is almost certainly asbestos.

AREA ONE from the bottom up:
Plywood subfloor
Glue
Sheet vinyl - will send to test for asbestos (very likely)
Black glue - Thin layer. Not troweled. Assuming it has asbestos.
Carpet
Carpet

AREA TWO from the bottom up:
Plywood subfloor
Carpet

AREA THREE from the bottom up:
Concrete - Can't confirm this but it's the entryway so it probably is concrete.
Slate tile - Original to the house. Very large stone tiles.

Can I glue down a floor over these areas? Would this "seal in" the black mastic in area two? Or what if I put down a floating floor? The black glue is intact and hard to scrape, but I'm worried that walking on the floating floors will slowly dissolve the glue and cause the particles to become airborne.

Thanks for any advice. I'm stumped.

There are a couple adhesives that now allow you to glue over the "residue" after wet scraping. But wet scraping over wood is not friendly.
A floating engineered floor is the way to go.
I'd double check the crawl space if there is one for dryness.

It's on the main floor and there is a basement below so moisture is not an issue.

The black glue is on top of a vinyl sheet so it will scrape off pretty easily. However, can I just leave it in place and put down a floating floor? Do you think the glue will break down; do I need to seal it somehow?

Also, each of the three areas will be slightly different heights, up to 1/4". Is that ok? Thanks!

You should leave the black adhesive and consider that it does have asbestos in it until you have it assayed. It will not break down, but will melt if it gets very hot.
Before you lay down any flooring you should check to see if the floor you are going over is flat with a straight-edge. You can buy a six foot piece of aluminum bar for checking. Where the floor has a difference of heights you should use some shim material to slope it up gradually. Scrape off any loose material where the existing flooring is high before you start to build up any low areas. It's important to get the existing floor flat to keep any warrantee from the floating floor. Cover the whole floor with plastic sheeting before you roll out any of the foam that goes under the floating floor. Then the engineered flooring goes down.
There will be better instructions that come in the flooring box. If you think you can manage the installation after reading the instructions, get a good pair of knee pads.