Upgrade old road bike to 7-speed rear derailleur? Just took my old 1983 12 speed out of mothballs. put on 94 miles this month very hilly here. My question is: 

can I upgrade my freewheel with Shimano MF-TZ31 Tourney Freewheel (14-34T Mega 7 Speed)? 

Would I also have to upgrade my chain, derrailer, and front gears?  currently have Shimano on it.  It was not a fancy bike no quick release on rear (just to give you an idea of cost of bike).  

I can do my own maintenance but I would need detailed part info not sure what goes with what. any help would be appreciated.
It is do-able at a reasonable cost if you do the work yourself. Your current derailleur likely does not have the tooth capacity for a 14-34t freewheel. The mount on a new derailleur wont mount to your bike if it uses the older style that is held by the axle nuts. Luckily there is an adapter available for about $5. Your chain will also be too short and too wide for for the new rear cog . The narrower 7 speed chain should work with your current crank. You will also need an appropriate freewheel tool and chain whip to remove the freewheel. A local bike shop may do this task for less than the cost of buying the tools. If you are using friction (non index) shifters they will also work. Based on average EBay prices of less than $20 each for a derailleur, chain and freewheel you will invest less than $100. The plus is when you are done you will know how to install and  adjust the derailleur, shorten the chain some basic tuning.