There are many overlay systems that work well with patched concrete. Staining and Polishing can also be done if the patch was done well. The difference in the age of the patch and the old floor may be an issue for just polishing, which is why I mentioned the overlay possibility. A 'skimcoat' is often a latex product that will not polish well. In this scenario an epoxy finish or overlay would be a better approach in my opinion. Somewhere like floridaconcretepolishing.com may be able to guide you further. Here is a link that might be useful: florida terrazzo repair

First time I've tried to resize photos on my phone so I hope this works. This is an outside door. It is 1-1/2 inch threshold. This is the one to the garage. It is 1-3/8 inch.

A heated basement slab requires plenty of extra planning before anything is poured. You will have to have a thermal break planned for (styrofoam is often used). Then you have to plan to have the hydronic heating tubes laid and then coated in concrete. You then have to have the concrete experts on hand for the last bit of the pour. The concrete aggregate used as a "finished" floor is NOT the same as what comes out of a cement truck. A special aggregate will be applied at the right time during the slab preparation. The guys will have to take plenty of time smoothing and readying the concrete so that a later date they can come back and do the polishing, staining and then finishing. As for heating the slab, it is a SLOW process to turn it UP or DOWN. On average, you can increase/decrease the temperature roughly 5 Celsius (9 F) per 24 hours. That means to turn it "off" it should take a 4 days. To turn it back on, again another 4 days. And going away for winter break? Don't touch it. Leave it be. There is nothing worse than frozen hydronic tubing that has burst because you wanted to save some energy. I've seen $25K spent on hydronic heating installed in a basement slab. The finished concrete will add another $5 - $25/sf to the build. And concrete in a basement is LOUD. The noise will bounce all over the place. Down hallways; up into the space above; under door jams; etc. The ceiling will require PLENTY of acoustic insulation to stop the up-down noise intrusion....especially with a "screening" room. You will want to contain the noise in the basement. I've seen concrete floors covered up within 7 years. Most homeowners find them "too hard" to live with (both "hard" and difficult because of all the noise).

It's true that in many jurisdictions, converting a garage to living space isn't permitted. However, if you live in a rural area or some place where it is legal, I have seen concrete floors that are stained and finished beautifully over large surface areas without any extraordinary slippage issues and fairly thin coating on top. You'll need to consult a professional coatings supplier to find out more, especially for a moist bathroom area. It's more common in high-end commercial structures such as car dealerships to see epoxy finishes rather than visible concrete since a slab must be in flawless condition to serve as a final flooring surface with a reasonably acceptable appearance. Epoxy finishes can be applied with additive flakes to help with slip resistance. However, if all you are wanting to achieve is an industrial vibe, there are so many tile choices out there that would serve you extremely well and wear better over the long haul than a visible slab or epoxy. With a skilled installer and rectified tile, grout joints can be as small as 3 mm (1/8 inch), and the large format tiles are becoming increasingly popular for homes, so the surface can have fewer lines than you might normally think about with an older tile installation. Porcelanosa and Happy Floors are two companies that have recently released new "industrial" tile collections with impressive finishes. These companies manufacture in Spain and Italy. The supplier ProSource, if there is one in your area, will have great wholesale prices on both brands as well as many others, and Porcelanosa has an annual fall sale, the last one 40% off, so you can get premium tile starting at $5 or so per square foot if you have time to shop.