Welcome to the board! Sounds like you have something very similar to my Masterbuilt offset. You can run it in a few different ways.
Yes you can cook on the grates that go in the firebox. in that case you're running it like a small grill, with direct heat. You don't need much fuel, and you don't involve the main cooking chamber (People abbreviate that to CC here).
Then the main mode is to have a fire in the firebox, and food in the CC. Then you run the exhaust stack wide open, and control the heat by choking the air intake on the firebox. The amount of fuel you need will depend on what/how long you're cooking. You'll just have to get the hang of it. I suggest you start with something easy and inexpensive like chicken, before you dive into bigger stuff.
(edited to add, look up the charcoal basket mod, it's well worthwhile)
Finally, you can cook with the charcoal tray in the CC. You can run it like a great big charcoal grill, like if you're grilling for a crowd. If yours is like mine there will be an intake vent at the bottom of the end with the smokestack; this would be the only time you use that. And you can set the tray higher or lower, to control the heat. The sweet thing about that is, you can run it like a hibachi again, with just a modest little pile of coals in the tray hiked up close to the rack. You don't need to have all the racks in it (mine has 3) so you can easily reach around the rack or slide it aside, the get at the fire.
For that matter, you can also run it as a little wood campfire under the rack. You can heat up anything you'd have over or in a fire like a dutch oven or a kettle. When you're done cooking, slide the rack away and whip out the smores.