Item 1: How to use trim.
When trim is set correctly, you should be able to center the stick and have a neutral nose (where it does not pitch, roll, or yaw. When airspeed increases, lift increases, so you would trim elevators down to keep the nose neutral. The torque of your engine and prop is a force acting on your plane. As you increase power, you increase torque, so you would trim aelirons to keep the plane from rolling when you center the stick. Another force that affects roll is center of gravity. If you are carrying an external payload that is not on the centerline of your plane, that will have to be compesated for with aeliron trim. Rudder trim is usually not needed in an undamaged plane.
Item 2: Manual trim "turns better" than combat trim.
True in part-
First lets consider high speed situations with a couple points considered. One: To simulate high load forces transfered from the control surface to the stick, AH will not let the stick respond when it is "heavier" than what the pilot can pull.
Two: Combat trim will trim elevators down as speed increases to try to keep the nose "neutral"
So when you are at a high speed with a high physical load needed to operate the stick, you are trying to pull up (and it wont let you) while CT is trimming down
Which goes to Schutt's example.
Now lets consider instantainious and sustained turns. As mentioned before, CT adjust elevator trim according to your speed. Lets compair what CT is doing to the elevators, to what you are doing with them in a turn. You pull a hard break turn and settle in a sustained turn. To do that, you pull back on the stick up to the point where you feel the onset of the stall, and ease off a tiny bit, and try to hold your elevator angle just below either blackout speed, or stall speed. As you slow even further, you will have to adjust your bank angle because the slower you get, the less bank angle you have avalible.
If you have CT on, it is adding another varible to what you need to do with the stick. As you slow CT is trimming more elevator. So as you are trying to pull the max elevator angle just short of stalling, CT keeps adding more elevator in spite of your efforts. Furthermore, CT does not act instantainous. With a fast speed change CT ends up chasing the proper trim setting.
I have no doubt that a player can get used to performing sustained turns with CT just as tight as a player not using CT. However, I am not convinced that CT does not (slightly) hamper instantanious turn rate due to its not keeping up to changing conditions.
Item 3: Trimming elevator tabs up will give you tighter turns.
With the exception of the high speed/high stickload case. False. The stall happens at the wing. It does not matter if you reach that stall angle with stick only, trim only, or anywhere in between. The max lift avalible from the wing is still the same