Plumbing – do about a toilet flange that is 1/4″ below the floor

The issues with the compression fitting have been addressed.

The brass flange fitting, the rubber gasket, and the threaded pipe is the "toilet spud". Replacements are available if the rubber is perished or the metal parts somehow damaged.

The flange nut looks pretty well bonded to the threaded portion. Soak well with WD-40 and let it soak in. There are splines inside the spud on which one would apply an internal spud wrench to keep the threaded pipe part from turning. You may find some other chunk of metal that will wedge against the splines, which in turn can be held by a conventional wrench. Holding the spud in place, remove the flange nut with a suitable tool.

Once the flange nut is removed, push the threaded pipe part inwards, but ensure it will not fall into the toilet. The part inside the toilet is conical shaped. Pushing it inwards will give enough free play that the rubber gasket can be pulled out. Once the rubber is out, there will be enough clearance in the toilet hole that the threaded pipe part can now be removed.

Examine the parts and evaluate if replacement is necessary. If the rubber is not too far gone, it may be possible to clean it, treat it with some sort of rubber treatment, and reinstall. If the rubber is cracked, hardened, rotted, or brittle, it will need to be replaced. The nut should be tightened firmly enough to ensure the rubber seals well against the toilet, but not so tight the rubber gets pushed out of position or the toilet gets cracked or broken.

Recheck the passage way that runs from the bowl to the horn. There must be an object lodge in there since the toilet flushed properly prior to the wax ring being replaced. Don't remove the toilet from the closet flange just yet. Insert a toilet auger and work the handle. It should advance through the toilet with little effort as it is being turned. If you encounter resistance reverse the auger while withdrawing it a short distance at the same time. Than continue pushing it forward feeling for any blockage. Withdraw the auger and flush to verify proper operation. If, after using the auger and flushing, the water doesn't flush pull the toilet, drain any standing water in the tank and bowl and lay it on its side on a plastic sheet. Examine the horn opening with a flashlight. If necessary insert a bent coat hanger into the opening and probe for foreign objects.