With a wire brush, and then sand, you use the sand to soak up the tar/diesel goo. It is a pretty easy process.

Yep it worked great, it got sanded and refinished, so it was a momentary pain in the ass to restore some Dade county pine floors. It is not like I mopped it with gasoline, Diesel is not explosive or highly combustible.

I have not tried it, but you could try baby oil or peanut oil. I don't know if it is because tar and diesel are both petroleum products that it dissolves it or if it is because diesel is a thin oil.

I had the same thing done at my house they put a liner down with tar mastic and then tiled over the wood floor. I tried everything and then remembered some words of wisdom my grandfather gave me about getting tar off of vehicles and that was diesel fuel liquifies tar. So after trying everything, I came up with a plan to get a mop and bucket, diesel fuel, play sand and a wire brush on a broom handle. I would mop the diesel fuel onto the floor, let it sit for a little while, hit it with the brush and it would come right off with no effort, but it would mix with the diesel fuel and make a black thick liquid. So I would throw the play sand on it to soak up the liquid. Then use a broom to move the sand around until it was too soaked to pick up anymore, then I would sweep it onto a shovel and dispose of that sand.

Every other way was an inch by inch method, you cannot sand it off, scraping it off does not work, and strippers do not lift it off very well. Using diesel to liquify it, was a smelly and messy process, but I did about 1400 sq ft. in a day this way, where as all the other methods I tried combined only netted me about 100 sq. ft over the course of several days.

Yes removing tile without breaking them is an art and honestly more time consuming than using a multi-tool to cut around the entire area, and then pry the entire tile surface up via the cut out subfloor as a single piece, then use a plywood the same size as the offset and glue the old subfloor to the new riser plywood.

If the subfloor is concrete you will have to remove them, you might want to see if you can find matching tiles to replace any that get damaged, or consider what you would like to install in the event that they do get damaged.

First thing I would do is pop those framing pieces and see what I am working with below the tile.