The flange is supposed to rest on the finished floor (but not higher). If it's up in the air, that's another story and would have to be fixed. Your toilet could be wobbling because the floor isn't level. If so, plastic shims from the hardware store will help.

Toilet installed and operational. I decided to put the wax ring on the toilet and set on the flange as a unit. This toilet is a low cost Glacier Bay from Home Depot and has a lot of quality look and feel and evens some "extra" parts. For one thing the closet bolts came with push on plastic washers that I used to hold the bolts vertical while I lowered the toilet. This is the first "extra" parts. Then on mounting the tank to the base the supplied bolts had the expected high-quality rust-resistant materials, and had the usual screw slot head inside the tank followed with a metal washer and a 1/8" (or so) rubber (or similar) washer. Then for the other end were the matching metal washer and nut. But, for some reason, more extra parts, regular steel-looking elongated washer and wing nut. The instructions did not go into detail on what this was for, but as it came in the package on the end of the closet bolts, I added them to the underside of the toiled lip...suppose they operate as a "lock-down", but whatever, I've never seen this arrangement before. Again, this is a very low cost unit, I'd expect fewer parts, not more. So far, so good.

I'm going to give you today's special, two answers for the price of one. If you must ask how to change out the flange,leave it alone because you will likly make it worse. Switching flange is a tricky chore for an experienced person. Using a masonry product suitable for thin setting,bed toilet in it. Here's step by step. Temporarly set toilet in place,measure gap between base and floor then trace outline of base on floor with sharpie. Remove toilet and cover outer rim and edge of base with saran wrap to prevent masonry sticking to it later. Put a 2"wide X twice gap measurement of masonry just inside tracing on floor. Prep bolts and wax then set toilet in place pushing down into wax masonry. I don't tighten bolts until masonry dry's but you can lightly tighten if you need more compression on wax. While masonry is still wet,remove squeeze out and excess saran wrap with single edge razor then smooth masonry with wet finger. When masonry is dry it can be covered with caulk if desired but I usually leave it as is and it look's fine if neatly smoothed.

Would you recommend a cemented PVC adapter like the ones above? Or something like this? Only concern is going right under the toilet (new Kohler Cimarron going in). https://www.supplyhouse.com/Fernco-3009-33-3-x-3-ProFlex-Coupling-Thinwall-PVC-to-Sched-40-PVC Also included a pic identifying the pipe, as well as the connection to the flange from underneath. Where would I be safe making a permanent, leak-free connection with that coupling? And klem1 - thank you, I was measuring out ways to do that, and turns out I would need to pull the flange awkwardly upward to clear the new floor... awkwardly angling the drain pipe (pulling more than I would like) and leaving the flange itself at an angle. So I think I'm going to have to replace the flange no matter what after all.