Getting it out of gear is easy...and isn't really an issue...it is a lot easier when the engine isn't under load (i.e. light to no acceleration) - stuffing it back into gear without the clutch wears out the synchros, but is nice to know how to do if your clutch ever fails (cable breaks, etc.)
The wobbling is the rear joint bushing & bolt under the car that connects your shifter to the shift rod. You can tighten it up a little, but if you get it too tight it won't slide and pivot correctly when you move the shifter....You really should remove the shifter, and unbolt it from the rod, and rebuild the bushing (there is grease and rubber o-rings and stuff inside the bushing), or buy a $30 short shifter at the same time. Most (but not all) come with fresh bushings, (my B&M re-used the bushing, but gave me grease and new o-rings
) then you just need to tighten it right so it is not loosey goosey, but still moves freely.
The shifter arm sits inside the shift rod fork, and when you tighten the bolt the rod fork gets squeezed and makes it feel tight...our 12+ year old cars tend to have a little play in them and it feels sloppy, sometimes tightenting that bolt a little helps..but again, not too tight, or it will be hard to move..