Re the battery I have the same problem in that mine is stored for 6 months in an underground car park without power available to keep the battery on charge.
If you leave with the battery connected you will run down the battery and likely shorten its life. If the car storage is secure then I lock the car using the fob with the boot open.Then disconnect the battery (-ve terminal) and close the boot and lock it manually.
If the car is not secure enough to do this then I would either remove the battery completely and also fit a thatcham steering lock (I use one which I store behind the passenger seat) or get a second battery and swap then over every couple of months and charge the spare one at home.
reposted from another post I made last year on another forum some other advise, pick and choose what you think makes sense:
I came across this guide
Original link (I have un-americanised it
http://www.mcoupebuyersguide.com/
Here are some of the winter storage tips I’ve come across. Some are probably more extreme than I’m going to attempt but worth mentioning anyway:
For Your Engine
NEVER start your coupe unless you plan on driving it for at least a half hour to get it to full operating temperature. It is far better to let it sit for 4-5 months than to idle the engine from time to time to “get the fluids running”. Doing so will just load the engine and exhaust with moisture and open the potential for rust.
Change the oil and filter – Oil gets contaminated during use and those contaminants can cause mild corrosion if left to sit for long periods of time
Top off the petrol from a quality station and avoid Ethanol if possible. Having the fuel topped off prevents condensation from forming in the tank and rusting it from the inside out. Don’t fill it to the top of the neck to leave a little room for expansion and contraction with varying temperatures.
Use a petrol preservative like Stabil to prevent the petrol from breaking down as well as preventing oxidation and rust formation. After adding it, run the engine for at least 10 minutes to allow the mixture to get through the entire system.
Before parking it for storage, take it for an extended drive to get all the fluids up to operating temperature in order to burn off contaminants in the oil and get rid of moisture in the crankcase and exhaust system.
If you live somewhere that rodents could be a concern, place steel wool or a rolled up scotch-brite pad in the tailpipes.
For Your Transmission
Leave your car in gear. Use wheel blocks to prevent it from rolling
For Your Brakes
Never set the parking brake. The brake pads could stick to the rotors or the cables could freeze or rust during storage. Use wheel blocks.
After the final wash, drive it around for a little bit frequently applying the brakes to dry them off well.
For Your Battery
Many people take their batteries out for storage as cool temperatures can reduce the life of the battery. Sitting for an extended period of time without recharging can also significantly reduce the life of a battery. For the Z3, I think it is ideal to purchase a float charger/battery tender to maintain the battery’s charge while it is parked. I’d recommend hooking it up to the leads in the engine bay rather than connecting directly to the battery in the boot. Classic trickle chargers if left un-monitored can overcharge the battery and also reduce it’s life. Float chargers, on the other hand, are designed to charge the battery to an optimal level then maintain that level without overcharging. In my research, I read good things about the following chargers:
BMW Advanced Battery Charger
CTEK 3300
Deltran Battery Tender Plus
For Your Tires
Slightly over inflate the tires by 5-10 psi to help avoid flat spotting from sitting in one place for a long time. This will also help compensate for the cooler temperatures.
Roll the car a few inches forward and back from time to time (without starting the engine of course).
Place cardboard or old carpet squares under the tires to separate them from the cold/hard concrete.
Some people choose to store their car on jack stands to take pressure off the tires completely, but this must be done right or it could cause more harm than good. Place the jackstands under the suspension so that all the bushings and springs sit as they do normally. Letting the wheels droop is hard on the suspension and exposes parts to rust that are normally protected.
For Your Exterior
Purchase a quality car cover for your Z3 to protect it from dust, moisture and dings while stored.
Thoroughly wash (including the undercarriage) and wax your Z3 right before storing it.
Be sure it is completely dry before covering it as moisture is your worst enemy.
To stop moisture from getting under the car, put a couple layers of plastic sheeting under the entire car and several feet to either side. It’s cheap and a good vapor barrier.
For Your Interior
Close all the windows and put the system on max a/c to close the outside vent. If the garage is heated, the window can be left open a small crack to allow air circulation.
Put a large bag of desiccant gel or an open box of baking soda inside the car. These will absorb excess moisture from the air.
Clean and vacuum the interior. Use leather cleaner/conditioner and vinyl cleaner/conditioner as required.
Do NOT use water on the carpets or seats right before storage or you risk mold and mildew.
Do NOT treat inside surfaces with Armor-All (or similar products). They contain a lot of water and chemicals that can encourage mildew and mold.
So there you go. It’s a little overwhelming at first, but really not too bad all in all. I’m new at this so feel free to chime in with comments and corrections.