How do I determine what the right size pressure tank is for my well?

To answer your question simply, yes, a pressure tank can affect the life of a pump. But there is so much more information needed to say what went wrong in your case. Static water level, pipe size, wire size, water quality issues like high iron or low pH. Could there have been a lighting strike, did your well run dry, do you have any sort of pump protection installed? Call a well company and if you’re not completely satisfied they know exactly what they are doing, call another one. A professional should be able to get to the bottom of your problem.

Size the tank so that you have one gallon of drawdown for each gallon of pump capacity. This ensures that the pump will get the proper run time. Run water somewhere until the pump starts. When the pump shuts off, drain the tank into a bucket until the pump starts. Measure the water in the bucket, that's your drawdown gallons. Then run water until the pump starts and time the time it takes it to shut off. Then run water and time the time until the pump starts, that time should be at least 60 seconds, and probably equal to the first time. If you catch one minute's flow into a bucket or any portion of a minute and multipy for one minute's flow, it won't be exact but close to the gpm of the system. If the pump doesn't stay off for 60 seconds, then you should get a larger tank which will provide a larger drawdown (equal to the gpm of the system) .

Yes it does. The larger the capacity of the tank, the less the pump will need to run. The pump however, should run for a minimum of about 2 mins. before shutting off. Typically, the bigger, the better here. It sounds like you need a bigger pump for that distance. A pressure tank only helps the pump from short cycling or running too frequently, which will protect and extend the life of the pump. If your pump can't build up the required pressure though, for the pressure tank's switch to shut off the well pump, then the tank is useless to you. Try going with more hp on well pump and/or a booster pump. Then you can size a pressure tank to cut in and out based on the pressure your pump will obtain.