You can cut off a chunk and send it off to a lab to test for asbestos content-- obviously, don't do that in an obvious place if you're not immediately planning on replacing it or covering it. If you can lift a baseboard and get material from the edge, then cover the missing section back over with the baseboard, that's often a good location. For the mastic, you can get it wet and scrape up some and send it off for testing. The lab will almost always have specific instructions on safe ways to collect material for testing and how much you need. Similar appearing materials are all over the place on actual asbestos content. Vinyl asbestos tiles tend to be square and have kind of a marbled look. They are often, but not always, 9x9. The vinyl asbestos tiles are generally quite low risk compared to the asbestos-backed sheet vinyl, because the asbestos fibers are bound in a matrix with the vinyl. Unless you pulverize them in removal, you're not going to get airborne fibers taking them out. If you contrast whatever your local recommendations are for VAT removal with sheet vinyl removal, they're usually pretty different-- the main thing people are concerned about with VAT is how you dispose of it. For sheet vinyl, though, they're really worried about how you take it up. Mastics can be pretty difficult to get up. For example, the black mastic was really easy to get up with Bean-E-Doo (whatever they call it now)-- anything else, though, forget it. The remnants of the Bean-E-Doo itself were challenging (lots of soap, water, scrubbing, etc.) However, though the same chemical said it works on old carpet adhesives, it didn't work at all for me. If you have things tested and the tile's asbestos and the mastic's not, the tiles are pretty easy to remove nondestructively with steam (e.g., a steam iron or a wallpaper steamer, or you can rent a big machine that heats the tiles for you). Then you can rent a big commercial scraper to get the mastic up, which is the most efficient. If the mastic does contain asbestos, either it shifts easily with heat or it doesn't, it's water soluble or oil soluble, etc. Use whatever people think is the best method for the specific type of mastic you have. Or paint over the mastic with one of the sealing compounds if the standard removal methods don't work. Since your tiles are loose, though, I'd take them out before putting any new flooring down.

My position on lead and asbestos isn't exactly popular here, so I may get flamed, bur I'm old enough that I think my decent health says I might be on the right track. I grew up in that era of "peak asbestos" that SJ talks about. It was probably peak lead, too, because every car on the road ran on leaded gasoline. I don't want to go back to those days, though, because neither lead nor asbestos is good for you. However, I do think that the dangers of both to the average homeowner have been exaggerated. Initially this was through sensationalized television reports, and more recently through overwrought social media posts. Let's face it, fear sells. SJ is right that a lot of building materials used asbestos, back in the day. But it wasn't the people who lived in the houses built with asbestos who got sick from it. It was the tradespeople who installed it and, even more, the factory workers who produced it. Casual and incidental contact with asbestos products in good condition isn't going to hurt you. You might not even be significantly harmed by taking a pry bar to a roomful of asbestos ceiling tile once or twice. That said, I strongly recommend that if you're going to work on building materials that you think might contain asbestos, you isolate the area where you're working with closed doors and/or plastic sheeting, keep an exhaust fan running in the window, and wear a good quality particulate filter mask. The more you're exposed to asbestos products being torn apart and beaten up, without proper protection, the more risk you take with your health. It's up to you where you want to draw the line with that, but I'll say that I've worked on a couple of asbestos-tile ceilings over the years, and I'm not very concerned about it. BTW, I was a bit amused several years ago when I was taking bids on having some asbestos floor tile removed. The 2 contractors who made the loudest noise about the asbestos both drove off in their trucks with their seat belts unfastened. :) As for lead paint, IMO it's a concern mainly if you have children or pets who might ingest paint chips flaking off, or chew on painted woodwork. I also recommend that you avoid sanding paint that might contain lead. Otherwise, I wouldn't worry so much about it. In most cases, you can just paint over it to seal it in. Keep that paint film in good shape, and you'll be fine.

You should go back to your certified training materials to consult the written processes on which you were trained.

Send it out to a lab for testing f you care. Random speculation from pictures on the interweb is useless-- get actual data. It doesn't cost that much. Or just assume it has asbestos and treat it as such.