Follow the manufacturer's rules. Underlayment was needed with older laminate flooring, as that stuff was so rigid and often did not have an attached pad, and you needed the acoustic cushion. The joints were tongue and groove, so once you locked them, they were vertically stable. More on bogleheads.org

The real issue is that the flooring is not made for that. If you add another layer of something that is semi-flexible underneath (not like a layer of plywood), then stepping on the planks can cause them to flex just a little bit more than intended. That, in turn, puts more pressure on the thin vinyl edge strips that interlock the planks, which can cause the planks to crack and separate. And then your floor is ruined. More on reddit.com

Yes. I've done it with and without. I regret the without. Every floor imperfection comes through. Unless you are working with a pristine floor with absolutely no imperfections, go with foam. Also, it is significantly louder. Vinyl flooring doesn't always sit on the floor on every square foot as it is floating, and not tied down. If you get a spot that bows up even 1mm, your eyes can't tell there is a bow, bit you can hear it slap your subfloor or cement. More on reddit.com

There's a difference between underlayment plywood (good) and underlayment padding (bad if already on your lvp). I think the contractor that wants to pull the existing laminate and carpet is saying to take everything off down to the subfloor, and add a new underlayment plywood (1/4" typically) on top to make it all smooth and the same height throughout. You're right that doubling up on padding is not a good idea. The new ply will give you the best base to start on, and the contractor recommending that sounds like the one that wants to do the job right. I'm not sure i understand the comment about raising the old carpeted area up "if necessary." It will absolutely be necessary if the adjoining laminate is left in place. Otherwise you'll have a 1/4" or 1/8" step down in the 12x12 area where the carpet was? Trying to match those elevation changes can be tricky. More on reddit.com