Supplying multiple devices from one battery
You might be able to get away with powering the coin acceptor directly from the battery, although the battery voltage will be a bit more than 12V if you charge it fully. Check the data sheet of the coin acceptor and the battery, to determine if the coin acceptor will be able to tolerate the max battery voltage.

The Arduino doesn't use much power, so you can use a linear volage regulator to power it. These are small, cheap and simple, but if you try to push too much current through them, they will get very hot. By the way, why do you need 6V for the Arduino? Can you not run it on 5V?

For the "5V 1A to 10 devices", do you mean 1A to each device, in other words 10A total, or do you mean 1A total? In either case, a buck converter (aka step-down converter) is probably the most appropriate tool for the job. Or you could use ten smaller buck converters, one for each device.

I bolded some keywords for you. If you google these phrases, you should be able to find the information that you need to get on with your project.