The fuel in a Cessna which has a "both / L / R / off" type selector will flow tank to tank if the selector is in the "both" position. In "L"/ "R"/ or "off" the fuel will be isolated to the respective tank. Though nice to be able to isolate contaminated fuel, it is unlikely that you'd be able to detect and then diagnose contaminated fuel in flight. More importantly, being able to use fuel from only one tank allows the pilot to: manage lateral balance, consume fuel very accurately from tank to tank for long range fuel planning (not really much a of a factor in two tank arrangements), and allow you to burn the remaining fuel deliberately first, if that tank is leaking, and thereafter isolate the leaving tank so you don't crossfeed and leak out fuel from the other tank. I've had to do this twice. On the "both" selection, the fuel between the two wing tanks can (and will) crossfeed and equalize through the fuel selector. If a tank is full, or overflowing because the aircraft is parked on a lateral angle, the fuel can also crossfeed between the tank vent spaces. This cannot be prevented by pilot action, other than assuring that full Cessnas are parked level, or slightly right wing low. Cessna 206, 207 and 210 do not have a "both" selection, and interestingly, you have to select through the "off" position to change tanks. This spooks pilots the first time they have to do that!
Yes, the low wing aircraft do not have a "both" selection for the reason stated, and more literally, because it is a design requirement that if there is to be a "both" selection available, the tank's vent spaces much be interconnected, and this is not possible in a low wing tank, dihedral wing arrangement. I think it's a better system anyway, as the fuel is always isolated, and it forces better pilot discipline in fuel management, and lateral trimming.
Yes, the lightest possible touch on the controls. You can always firm it up if needed. Death grip is never required. If you're gripping the controls too tightly, your own muscle competition within your hand and arm will mask valuable force feedback which will be coming through the controls. Let the plane tell you what it's doing first, and then you impose your control over that, rather than in spite of it!