First press control and f and do a search for words like laminate and pergo for lots of info in other posts.
I wonder why you want the insulation on the floor to start with. If you have no moisture coming through the floor and the basement walls are insulated and the space is heated, then I don't see a whole lot of need for what little you will gain in a feeling of warmth to your feet. If you want floor heat then use electric or water radient heating or put down carpet for a warm feel. But I will leave it to your call. I wouldn't worry about 2by sleepers on the floor and am not sure glue is even necessary (or use very little)since the laminate floor floats also(it isn't nailed or screwed). I agree with Suzanne that the thick styrofoam may be bouncy to walk on. Lay a sheet of it on the floor and a sheet of plywood on top of it at your lumber yard or home cheapo to test it out before buying(I wouldn't be afraid to do it before buying or find a different store). Most laminates require a thin foam rolled out underneath. If you want more, maybe try some of that thin folding foam insulation that goes behind siding also.
Warranties. Be concerned and follow directions but most of them are written so that you will probably never collect or collect enough to be worth the trouble so do what you want.
Finally remember laminates are just floor coverings that wear out and need replacing later. They are susceptible to scratching and water damage which is why many people don't use them in bathrooms and kitchens. That said I personally wouldn't be afraid to put it in a bathroom or kitchen knowing it may be replaced when water damaged later.(I put carpet in bathrooms and kitchens knowing it will be replaced later also) Others will chime in with varying opinions but in the final analysis, do what you want after making an informed decision. Good luck.