How well the blunt end of your cutter works for tapping depends on how small that end is. The screw cap on Toyo cutters is enormously too large to be used for tapping. Some old style glass cutters had a ball on the handle end. Those are fine for running straight lines but considerably too large for curves. The old style metal cutters WITHOUT a ball end are perfect. If you can't get one of those, a Phillips screwdriver (X end) works beautifully. The object is to have a tip small enough to be able to strike ONLY on the line to be scored.
As pointed out by Moonraker, you MUST tap on the back of the score. Although some tappers hold the glass upright while tapping, you'll have much better success if instead you lay it down flat while tapping. Tapping will often cause small chips where the glass breaks. To ensure those chips are only on the scrap side, tap just slightly (about 1/16") on that side. (another good reason why a small tapping head is helpful). That way all the chips will be on the side you plan to trash and the other side will have only small overhangs that can easily be taken off with a carborundum stone or on a grinder.
If you're having trouble getting the pie pieces to start coming out, it helps to score another concentric circle about half the size of the original one. The smaller the pieces inside the circle, the easier they start popping out. You're right - once the first is out, the rest fall away.
As to other possible shapes - just about anything. Another demo I like to do is to debunk the opinion that you can't cut a "V" into a piece of glass. Take your cutter and score in from an edge, stop, turn the cutter and score back out leaving a 90 deg corner. If you're patiently careful, you can tap out that piece. It CAN be done, but it's NOT something that should be done. The remaining piece WILL break out from the "V". It's an effective way to demonstrate why saws shouldn't be used for conventional stained glass. "Any cut that can't be done by hand, shouldn't have been done at all".