Railways can always give experimental stoppage at Alwar, agreed.
As for skipping Jaipur, it's possible. It does not matter if a stations is A+ or not. Even Bhopal and Delhi Jn are skipped; can't see a reason why Ajmer and Jaipur can't be skipped. They may be important tourist centres, but if they are not getting passengers from those stations(due to inconvenient timings maybe), IR can make ADI Raj skip those stations.
Regarding BCT-NDLS Raj; maybe food/crew change is loaded from base kitchen of Kota, hence stoppage is required.