Answers

Yes, you can paint vinyl shutters. First make sure they are throughly clean and dry. Then is they are glossy give them a light skuff up with a scotch bright pad or fine sandpaper. Finally I would recommend using a spray paint that is designed for plastic. You can buy this at most home improvment stores. Do a test spot first and make sure there are no reactions.   

I would start by performing a flow test at your shower head. Get a 5 gallon bucket and open your shower head full open and time how long it takes to fill bucket. If you fill the bucket say in 1 minute, this means you are emptying 50 gallon tank in less than 10 minutes. (Divide 50 by number of minutes) Keep in mind as you use hot water, it is replaced with cold water, so hot water temp is dropping from the moment you start. Secondly, you most likely temper your hot water with cold which then extends this time. In short this is just a guide but tells you how long it takes to empty tank. If this works out that your emptying bucket in shorter time than your shower, concider checking flow restrictor on your shower head. If this is not the case then call the installer of hot water heater.