Managing tiled basement floor, short term and long term

My basement floor is a concrete slab with 1’ square vinyl tile. Two thirds was done more than 30 years ago with troweled on mastic and tiles having no adhesive, and one third was done maybe 20 years ago with peel-and-stick self adhesive tiles. A few of the self adhesive tiles are coming up, and there’s white powdery residue between them and the concrete. They are trip hazards and I’ve been cleaning the concrete and tile with a super coarse scouring pad and then sticking them back down with contact cement, which seems to work.

But I’m worried I’m using a counterproductive approach in the long term. It’d be nice to have more durable tiles some day, or even some other hard durable surface such as epoxy. (Not interested in carpet or wood.) How do they remove old tile, just kind of chisel and pry it up? Will the contact cemented ones cause a problem? Will the older tiles, almost entirely still holding fast, become impossible to remove? Should I be making temporary repairs by a different method, until such time as I hope to have it all redone?

My basement has never flooded. It has a perimeter drain and a sump, but I’ve never seen water in the sump and it has never had a pump placed in it. However, I’m told many houses built by this builder do not have vapor barriers because they saved money by not bothering, as the owner can’t tell whether it’s there once the concrete is poured.

Thank you!