How long will a 12v/ 2.4 Amp battery last if you use an appliance which uses 0.8A ?

Answer 1

You need to know more than that.

A battery has also a "capacity" number, usually expressed in mAh (milli Amps per hour) which shows how many milli amps the battery can provide in one hour, provided it is fully charged.

For example, given the same load, a big car 12V battery will last much longer than a 12V battery the size of matcbox