yes the laser will cut paper and cardboard.
We use the Lightburn software to setup and sent jobs to the laser cutter. For cutting you will need your artwork in a vector format like .DXF, .svg, or illustrator .ai
The laser bed size is 1200x900 from memory, it's definitely big!
In the past I've found you can cut a few sheets of paper stacked up if you want a bunch of copies.
Also the bottom of the paper can get little burn marks from the laser beam hitting the steel honeycomb cutting bed.
Placing a sacrificial sheet of paper or cardboard under the one you want to cut prevents those marks.