Hi,
When the stick is pushed up, the fork in the shift rod will rub in the groove it's riding in. Normally, the fork will "float" within the groove, with minimal friction. What you are probably feeling is the friction that you are generating. Same is true for any gear, in general but it will depend on fork length, bushing design, etc.
The bobbing back and forth of the stick as you lift off or apply throttle is also normal as a box ages, in my experience. Others with more detailed Getrag expertise may offer more insight and I might be proven wrong. The torque of the engine causes wind-up in the gear train and this can result in fore and aft movement of the input shaft, which you notice as a movement of the stick. Remember that the gears are helical, and the screw action causes axial force.
What fluid are you using, BTW? I switched to Redline years ago and have been very happy with the results. You will encounter a heated debate of MTL vs. D4ATF (it's like Coke and Pepsi) but I went by Getrag's recommendation. There is a sticker on the bellhousing, visible from the engine compartment, that tells you whether your tranny uses ATF or gear oil. Mine required ATF.
Hope this helps,
Adnan