If laminate is fitted right up to the skirtings, then an expansion gap should be left.... 10mm usually,but with thin laminate, you could get away with 5mm.
Run a bead of clear silicone (or brown, whichever you choose) along this gap, on the surface and against the skirting. This is done to stop water (from spills/cleaning etc) soaking in under the flooring. This will also keep the flooring in place. Send the ends of the laminate under the plinths as mentioned above.
Bear in mind that anything too thick might make it impossible to pull the appliances in and out.
The problem with thin laminated "lifting" in the middle of the room is well known. Perhaps apply some glue or silicone in several places as it's laid.