Is it possible to have underlay and carpet fitted on top of laminate? Or do I really have to lift it all up ?
Not ideal to have layers over layers but there shouldn t be a problem.
Better to take off old stuff and lay new one.
It is possible. I would check door clearances and skirting height before attempting this.
Its not ideal, saying that if the laminate has been well fitted and has no lose or moving parts, then yes it's possible.
I would not recommended installing carpet on top of laminated flooring. Laminate is a smooth floating surface and will cause the carpet to slip and move resulting in your Carpet stretching over time. The removal of Laminate flooring does not take long and will save you money in the long time. So it's not worth try to just to save time.
As long as you don't have more than a 20mil gap around the laminate so that you can fit the grip per and as long as your flooring is not bouncing to much then it's not a problem