Kreg joints - Minimum thickness material?

Yes...you can do 1/2" with no problem using the correct bit setting and the correct screws.

Yes....that's the bit size but the jig is set to the correct angle and depth of the bit for the material.

I had to dive into the scrap bin to find something as thin as 1/2" to do the test but I can verify that the Kreig worked fine with it. This was with oak so I guess that if the material you are working with is fragile enough it might not work so well. Odd that it took me so long to figure out how to set the Krieg for the thin stock. I have two drill bits with the collars pre-set and seem to never actually change the setup and it took me several minutes to figure out what I was doing.

I have done it on several occasional making jigs out of 1/2" Baltic Bbirch ply.

Keep in mind that Kreg also makes s smaller jig and drill diameter also. I did no use that however, the 3/8" bit worked for me Test however.

I doubt you will get a lot of strength from Melamine, however, since it is particle board. Might work, though. But as the shelves might sag over time, the screws might break through the Melamine down the road.

Another option is to have some mechanical joining, such as a spline between the melamine and aak. Biscuits might work, but I'd test that first since the biscuits swell once the glue is applied and might blow out the particle board.

I think I made a desk some years ago with Melamine shelves and used oak trim front and back to add stiffness so that they wouldn't sag. I used a spline and it worked well.