Hi,
You should not have to pump the gas 10-20 times to start the car if you are starting it often. If the car is sitting for a while then maybe 5 or 6 times and that's if its been sitting a while.

The pump is a mechanical pump and should start sending fuel as you crank. You can switch to an electric one to avoid this but you will need to power it.

Glass bowl is a original style and there are reconditioned ones out there. I have used them and they look great but for daily ease of use stay away from them as they tend to leak. Any parts store can give you a non-glass bowl one to fit your care easily.
Good luck.