How many internal 3.5" drive bays does this server case have?

This server case has 4 internal 3.5" drive bays.

What type of motherboards is compatible with the iStarUSA D313SEMATX-DE1BK server case?

The iStarUSA D313SEMATX-DE1BK server case is compatible with Micro ATX motherboards.

Will a standard power supply fit, or does it take a special PS?

It uses a regular old ATX PS/2 sized PSU that are in 99% of desktops.

What are the case dimensions? I can see the dimensions of the box in one of the pictures but I can't find exact case dimensions here or on iStarUSA's website.

A rack unit is a standard measurement of 1.75", so this 3U case will be 5.25" tall. Rackmount equipment is 19" across unless stated otherwise. This leaves only the depth to find. I had some trouble finding the info initially, but according to the manufacturer's site this case is 16" deep. Overall dimensions: 19"x16"x5.25