Changing from 5 to 6 cog freewheel on 1986 Stumpjumper-Sport
(axle width) Maybe, there is a pretty good chance your bike is already at 130mm O.L.D. spacing. Road bikes would be at 120 or 126mm from that era, but a mid 80's MTB has a reasonable chance of being at 130mm. 


http://sheldonbrown.com/gloss_n-o.html#old 

2-3. All chains for geared bikes are 3/32 interior dimension, the difference between 7-11 speed is the outside width. You should buy a new chain if you buy a new freewheel, any quality 8spd chain is fine and should work on your current chainwheels. 


For an MTB derailler 30 -> 34 should not be a problem. You will likely need to make adjustments to the B screw to make sure the cage clears the largest gear. 


http://sheldonbrown.com/gloss_ba-n.html#btension