When I flush our toilet, the water (etc.) in the bowl rises very high, almost to the lip, before it all flushes down. It always flushes, and it doesn't sound like it's "straining" to flush, but it doesn't seem normal for the bowl level to rise so high before flushing. Could this have anything to do with the flapper valve, or is it more likely a clog somewhere below? Thanks in advance.

There is a clog that is causing this problem. Try using a plunger and see if that does not cure the problem. The clog will only get worse and then your bowl will overflow if not cleared soon. Flappers don't cause this kind of problem.

This will be speedball1 last post for awhileIt could b e a clog but first read this. I have one that most repair plumbers miss.. Look down at the bottom of the bowl. If there is a small hole, then that is a jet that starts the syphon action. If it's clogged the water will just swirl around and slowly go down leaving solids behind. Take your finger,(UGH! ) and run it around the inside of the opening. Over the years minerals build up and cut down on the syphon (flush) action. If it is rough or you feel build up, take a table knife and put a bend in it to get around the curve in the bowl and chip and scrap it clear. Next take a coathanger and clear out the holes around the rim. They start the swirling action. And last, check the water level in the tank. It should be 1/2" below the top of the over flow tube. And speaking of the overflow tube, Make sure the small 1/8" tube from the ballcock to the white overflow tube is connected so it discharges in it and that it's flowing when the ballcock fills. This is what raises the water level in the bowl. For a good solid flush they all have to work together. Hope this helps . Tom