Consider any cutting tools as sacrificial, when it comes to Melamine.
It's bastard hard.
It also needs brand new cutting tools to cut without chipping.
Masking-taping the cut line may help a little here.
Also, the dust produced when cutting it, is deemed highly carcinogenic.
Extract, like your life depends on it.
It has a reasonably low co-efficient of friction, and is robust enough to have softer materials slid over it on a regular basis.
As long as you are using self-adhesive Melamine, you should be ok.
If you are using wet-adhesive, you'll need to apply a balance sheet to the opposite side of the ply - otherwise it'll most likely bow - there's remains a small risk of bowing when using self adhesive Melamine - even though that doesn't contain as much moisture as a wet glue does.