Unfortunately, the really good time to do the initial preparation of that floor for a tile installation woulda been before you had those nice window walls installed.
It's gonna be messy. As Brian points out, the paint must be removed and it must be done by mechanical means. Generally referred to as scarifying, it involves grinding the surface down to clean concrete. Can be done with a number of different tools, but for a large area you might wanna consider renting a serious scarifying machine or even hiring the job done. Looks like you've got a bit of floor to do.
The cracks in the concrete need more description and you'll likely need to wait 'till the scarifying is done to see them all. Are any of the visible cracks higher on one side than on the other? Even the tiniest bit?
Have you used a long straight-edge to determine how flat the floor is?
Your first 1 thru 10 list is in the ballpark, but we'll get to all that as you go along. Have you purchased the slate? Do you know its origin or quality?
The trowel size and type of mortar will depend to a large degree upon the flatness of your floor and the gauging (variation in thickness) of your tiles.
In the second 1 thru 10, most of that can wait a bit, too, but.....
1. Your substrate and your tile and your tile installation products and your grouting products and the ambient air temperature must
be 50 degrees Fahrenheit or higher at time of installation and remain at or above for at least 72 hours after completion.
2. Tile don't give a rat's patooti how level the floor is, only how flat.
5. I'd recommend at least 3/8ths" for that area.
6. Once your layout is figured and marked on the floor you can start tiling anywhere you like. You can find out a lot more about that here on the site.
8. You do not ever
want tile edges touching anything but grout or flexible sealant. Never. For those perimeter joints at the outside of your floor you must leave a movement accommodation joint, again I'd say at least 3/8ths" for that room, which can be filled with an appropriate flexible sealant. Given the shape and exposure of that room, I'd suggest you'll need such a joint dividing the two sections, too. More on that will come later.
In what geographic area is the house located? Which directions does that room face? What are the overall dimensions of the room?
That should get us started.
My opinion; worth price charged.