That does sounds weird. And it seems that you really do have something going on with the brakes.

Did you have the booster or the master ever replaced? The reason I ask is that the booster pin (The pin that the pedal pushes) could be too far engaged and partially locking your brakes. Not likely but it could happen. You need to look at your calipers while someone presses the brake pedal and you need to see movement. The pads also need to move freely in their spot.

For the pedal sinking to the floor, that is really bad. It could happen if you have a leak or if the MC is on it's way out.