Teepers,
If you have wooden dowels for pushrods it's not going to hurt anything if they rub against a fuselage former.

Not bracing pushrods tubes probably won't hurt anything in a trainer airplane, as there isn't too much force on the control surfaces. But not bracing is a bad habit to get into. You should always try to brace this type of pushrod setup. What happens on more aerobatic planes you will find the plane is weak or "mushy" when using the control surfaces. What happens is when you move the control surface the pressure on the surface is enough to cause that un-braced pushrod to flex, and then the control surface has less authority..

Hope this helps

Ken