Open the case, it is safe to do while the system is running ( as long as there's no bats or anything flying around your room ) and read the label on the psu.
At that point you can also check it's dimensions.
1. Google your PSU. Simple. It also should have information on the side or bottom of the PSU. Should come under 12v Rails
2. ATX is the standard PSU and Motherboard, any ATX PSU will work in an ATX or Mini ATX Motherboard, with either a 20 pin or a 24 pin connection. Most PSUs nowadays have a 20pin Connector with an extra 4pin one for the 24pin motherboards, so there arent usually issues with fitting.
3. Yes. It is safe, but not recommended. The normal method is to remove the Power Lead and wait for the Motherboard LED to turn off, this will signify when your PC has no power going to it. Then remove the case, and tinker as much as you like