If you have a battery that is corroded, it's leaking. It will eat a hole in your car. And it won't take long. And that spot where the battery is structural underneath so get yourself a new battery.
And the advice about the baking soda solution - water mixed with arm-and-hammer - is good advice. That neutralizes the acid and will help you clean off the car under the battery. Take the battery tray out while you have the battery out - it's only a couple bolts.
Clean it out good.
Put the battery tray back in.
Put in a new battery. I like Optima because they are gel-cells and don't leak, and generally last longer.
Before you reconnect the clamps, use a brush to clean the terminals - they make a special one for batteries.

One part is for cleaning the battery terminal; the other is for the inside of the battery clamps.
When you get the battery back in you will have a few little jobs to take care of.
- Radio memory may be erased (saved stations, preferences etc.)
- You may get a BAS/ESP warning light - don't panic - it's easy to reset:
If the power supply was interrupted (battery disconnected
or discharged), the BAS/ESP malfunction indicator
light may be illuminated with the engine running. To
re-synchronize the ESP, and cancel the malfunction indicator
light, the steering angle sensor will need to be
recalibrated.
1. Turn the ignition switch to the ON/RUN position.
2. Rotate the steering wheel to the center position.
3. Rotate the steering wheel completely to the left, and
then rotate the steering wheel completely to the right.
4. Bring the steering wheel back to the center position.
5. The BAS/ESP malfunction indicator light will go out.
If the BAS/ESP malfunction indicator light is still illuminated,
the vehicle should be serviced at an authorized
dealer.
(manual, p76 - UNDERSTANDING THE FEATURES OF YOUR VEHICLE)
There may be other things but in my experience, that's what I found.
Don't put off getting the battery. Running the car without a good battery puts stress on your alternator and can damage electrical components that require proper voltage.