The replacement MPU is even cheaper from nvram.weebly.com. There is eBay fees built into the price there.

The corrosion looks pretty minor, but if you have never soldered on a printed circuit board before i wouldn't make a corroded bally MPU your first go at it. Make sure your power supply is good. Need +5, +12v and +21v at (original) MPU test points to boot The connectors are usually bad in these games. top right driver board, lower left MPU, and the rectifier board is the biggest problem connectors

Photos 3 and 4 are an electrolytic capacitors on your sound board. He is not a battery, but does hold a charge. He keeps the 12v power on the sound board up/smooth/clean.

Yes the battery is mounted at the bottom of the mpu and is missing from your board. You are using a normal static ram. The data will corrupt every time the game is powered off, but the game is still playable without a battery.