To answer your questions in order
1 - correct exposure is the best way to make your screens last longer. Underexpossed screens will wash out when cleaning. Also you must make sure that your emulsion is suitable for use with waterbased ink.
2 - waterbased ink is prone to drying in the screen. The only surefire way around it is to keep printing without too many breaks. Don't cure on the platen, as the heat will also cause the ink to dry in the screen. Some ink brands make a 'retarder' additive to slow the drying down.
3 - if you have room to place the wet shirts then you are better off printing a batch and curring all together. Some ink brands make a 'cold cure' additive so you do not need to use a drier. It won't give as long lasting print as heat curring but it is ok.
Speedbase ink is only really a hobby brand, but is ok to start with.