BMW: 1987 BMW 325i coolant issue and others, coolant tank, water coolant

Question
I just bought a 1987 BMW 325i Convertible.  It has 248k miles and comes with a few problems, the most concerning is the tendency of the engine temp to go to the top of the red-line within 5-10 minutes of driving, sometimes less than a mile.  I thought the thermometer might be broken since it wobbled left and right sometimes; also I turned the heater on full blast to cool the engine, but after a couple of minutes the heater only blows out regular outdoor temp. air.  I realized that the water/coolant resovoir seems to be leaking down in the engine compartment.  Will the fix be as simple as a new coolant tank?  What is the proper coolant/water ratio for this engine?

Also, there seems to be a slight oil drip when i park the car, not too bad but several small drops... what should I check first to fix this?

Answer
Patrick,

 First and MOST importantly, if you want this car to run at all, you CANNOT drive it while the temp is high.  Even turning the heat on will not help a over-heating engine, especially one that is low on coolant.  

 And engine creates heat from the combustion process, and as a means to remove this heat, water/coolant is circulated inside passages in he engine to remove this heat.  The heated water comes out of the engine and flows through the radiator where the heat is transferred to the air.  
 If you are low on coolant, your engine cannot remove the heat from the engine, and over-heats.  When an engine overheats, it warps things.  Metals expand under heat, and sometimes they dont go back into the right shape, and you blow a headgasket or crack the head.
 
 So obviously you want to keep the coolant tank full, and if the coolant tank is full and the engine is still over heating... then check the thermostat, or replace it to be on the safe side.

 Cooling systems are simple, cold water in, engine heats water, water carries heat out of engine, radiator cools water back down.

 I would mix coolant and water 50/50.  If you are off a little its not going to hurt anything.  They make a tool that you can check a sample of your coolant and see the antifreeze content with, it's less than $2.

 So I would replace the leaking coolant tank AND thermostat.  I could do both of these jobs in 15 minutes, so they are VERY easy.  Then fill back up and bleed the air out of the system.

 Hope this helps,
 Josh