Can I use a car battery for running DC motors?
The car batteries are designed to supply 300 amps or so for a few seconds. They would not ordinarily be discharged more than 30% or so very often. They will not last very long if they are discharged nearly completely every time they are used. There are batteries that are very similar to car batteries, but they are designed to be discharged more completely every time they are used. They will not do well at 300 amps, but that is not what you need. The proper battery is called a deep discharge battery or a marine battery.

Marine batteries are not widely available for 24 volts, so you will need two connected in series plus to minus just like flashlight batteries.

You are not going to get electrocuted by 12 or 24 volts, but you could be badly burned or even explode a battery is it gets shorted.

Two fully charged batteries connected in series should provide 25 or 26 volts with no load. Loaded as you propose, the voltage will be closer to 24 volts. The motors will just run a little faster or slower if the voltage is a little above or below 24 volts. As long as the motors don't continuously draw more current than they are rated for, motor power should not be a concern.