Feeding them by hand can often get them more comfortable with you, and it's certainly worth a try. If you are worried about biting, you can start off by holding the food on the tip of a pair of tweezers and wiggling it around under water to get attention. After a while of doing that, you can probably start using your fingers. That's one method of doing it.
My turtle is very comfortable with my presence, but she is also now 2+ years old and I have never hand fed her. It just takes time ...
As for water, frequent water changes can "hurt" your turtle and ultimately your bacteria cycle if you have one established. What is your setup like? How big is your tank, what kind of filter?
If you change your water too frequently and have a bacteria cycle, it will kill off your bacteria, but you need the proper filter to get a good bacteria cycle going. If you just have a stand-alone tank, changing it too often gets time consuming and things like chlorine in our water supply can chafe at the turtle's skin. If you don't change it enough, the breakdown of turtle waste will become smelly and ultimately have to many nitrates/nitrites in the water which can again chafe the skin or hurt the eyes.
I would recommend taking a good look at your tank setup and reading the recommendations on the parent site (
www.redearslider.com). For instance, my tank, I clean out my filter every 6-8 weeks and do a 25% water change every 2 weeks or so, and fill up the water due to evaporation as needed. I *never* clean my tank because the filter does it for me! But with a larger tank (currently 40 gallons), it's just not an option to dump it out and refill that often.