You new installation will only ever be as good as what is there now. If you are willing to take that chance, then following the above advice should be sufficient. Additionally, if you do not have an voids to fill, instead of patching you can use a liquid primer to facillitate a good bond if the existing tile is asbestos. It its not asbestos, you want to scarify (rough up) the surface with a heavy grit sandpaper to facillitate bond. If there is any wax coating on the existing tile, that wax should be stripped before scarification, patching, priming, or installing new tile.

Ya'll are making me blush! lol!! Seriously, I really do appreciate all your kind words. It makes me smile. Cotehele, my sunroom is not heated either. I did isulate it well though, so I can keep it comfortable with baseboard heaters in the winter and ceiling fans in the summer. The window is a standard exterior window with insulated glass. It is 4' wide and 3' high, a slider. It can be used as a pass-thru to the sunroom. The window has built-in J-channel trim on the outside (like you'd use for vinyl siding and we installed the drywall into that channel. The whole sunroom is drywalled. I can take a picture of how the window looks from the sunroom side this evening, if you'd like more details. If I had it to do again, I'd get a taller window that went all the way down to the granite countertops. I LOVE the way that looks and it would have been easier to pass things through there at a lower height. Cindy

I also would advise just doing the wood flooring throughout. If you get good, high end materials wood is surprisingly durable and the new technologies make it a lot more maintenance-free than past products. FWIW I also live in Florida and have engineered HW floors throughout my house including the kitchen and our DR which has French doors that lead to the backyard, and which is the main entry area for most of my foot traffic. Haven't had any problems with dirt or moisture anywhere. Also, if you may be thinking resale it will be a lot more desirable to have the same nice flooring throughout the house. Someday you may have buyers who look askance at two sections of a house with different floors, especially since you say your choice is somewhat unique and would be hard to match down the road. So my advice is get a rug for the craft room and a leak-proof pan for your washer and go with the hardwood. Ann

The correct way to do this is to replace the old flooring. Unless you put something over the edge of the linoleum, it will start to peel away from the subfloor. It is just a matter of time. An easy to do flooring would be to install vinyl click lock flooring right over the old flooring. (Frequently called LVP - Luxury Vinyl Plank) You should pull the toilet and reinstall after the flooring is in.