Idle is well covered i know, but i search and never seem to find what i want, can someone please put a howto up on searching correctly

Anyhow, among the many many problems my omega has is one thats really starting to get on my man boobs now, it cuts out, never when ticking over - only when i could least do with it i.e slowing for or on roundabouts/junctions or sometimes when braking towards a junction it will stall or jump into first just as it is stalling?
I cleaned what i beleive is the icv? (on the battery side of the engine, breather goes in one end and it sort of plugs into the engine with a large rubber pipe??

sorry am crap at descriptions!)
I also did the thing in the large hose from the airbox to the engine (maf or afm or fam

)
I know the aux belt needs changing as it slips when cold or really wet and was wondering if that would cause the alternator to drop the voltage it supplies to things when slowing and cause it to stall? Its a '99 3.0 elite auto btw

I also know the gearbox switch needs cleaning too as it throws up automatic gearbox if started in p but is fine if i start it in n and dont know if that could be the cause?
Also will it cause damage if when it stalls i knock it into neutral and fire it up then select drive again whilst moving???
Thanks in advance you lovely lovely helpful people

Mick