This problem is common with the Delta brand faucets that use the ball,spring and seat set ups.
In most cases this can be remedied by removing the handle and tightening the little plastic ring you can see just on the inside rim of the bonnet with a screwdriver.
(they actually make a tool to tighten this that comes with the inexpensive repair kit)
this little plastic ring just applies more tension on the rotating ball to the small rubber seats which will stop the leaking under low water pressure conditions.(check the tension of your handle while tightening! If you overtighten the ring, it will make your handle too stiff to operate…you want just good smooth action!)
If your up to the task you should just rebuild the whole inside of the thing!
costs only a couple bucks for the kit, and it will have the handy dandy little tool I spoke of included and even some instructions!
The drain problem your having is a MUCH bigger concern!
Is your shower fiberglass or tile?
If its fiberglass and you dont see any obvious cracks, you may just need a new rubber compression gasket.
Look for a manufacturer name on the stall…florestone is one of the larger manufacturers of fiberglass shower enclosers and the rubber compression drain gaskets are easy to obtain and install.
Hopefully thats all it is!