What kind of battery (size) do i need for replacement

Buy the replacement part first and whatever tool size fits is going to be apparent.
The oil pressure.temp. sensor looks like a spark plug (kind of) . one wrench... whatever size...
DO NOT overtighten the replacement... it is a tapered threaded sensor ... and will damage the block if overtightened.

need more info what kind of car or truck, year, engine size

Measure your old battery for size. Check to see what the cold cranking amps are on the battery sticker. Check to see what kind of cable connections it has then buy a matching battery at any automotive store.
Or just tell the guy at the store what year and make of vehicle you have and they will get you the correct replacement battery.

In most cases they're specialty batteries. Stop in a Batteries Plus store and they should have your battery and usually are more than happy to put it in for you

Yes, you can replace them. They are a security 12 volt. Most parts stores would carry them. Best to take your remote apart, and take the battery with you.

The official size is call Group 34.

G34

Just ask for Group 34 or G34 size battery from your part store.

Here's a link to Sears Die Hard site HERE

They should have a look up book, or have it online. No need to have any numbers for them.

where ever you buy a new battery they will have the sizes to fit your car.

Depends on your funding. If you can spend a little more, get an Optima Red Top - they're between $110-130, but they're fantastic batteries. Tremendous power, very high cold-cranking amperage (upwards of 900 amps), and very fast recovery time.

The main thing to look into is the cranking amperage and the cold-cranking amperage (these are listed on the battery's label). The more the better, so get as much as you can afford.

Your car should have came with a card about the size of a credit card. It is located in your manual book.