Most of us live "so far away from all those records"! Fortunately microfilms of many of those records can be viewed at your nearest LDS Family History Centre - a full list of Centres in Australia can be found at
www.familysearch.org.
But Hunts is not the easiest county to research as the LDS was refused permission to film many parish registers, so these can only be viewed at Huntingdon Records Office (who also provide a research service at very reasonable cost for those like us who don't live within easy travelling distance of Huntingdon). Unfortunately Stilton and Yaxley are two such parishes whose parish registers have not been filmed.
Whilst you do not mention if and how you're connected to the Griffens in Stilton in 1841, in answer to your questions
1. You go back generation by generation using parish registers, where baptisms, marriages, and burials are recorded.
2. If you mean Griffens living in Stilton today, it's possible, but who knows?
Hunts Marriage Index has a marriage in 1827 at Stilton between Robert Griffen and Elizabeth Ruff, both of the parish of Stilton.
Living in Yaxley in 1841 were James and Sarah Griffen, 58 and 60 respectively, who are just about old enough to have been Robert's parents. But there's also a marriage in Yaxley in 1792 between Robert Griffen and Sarah Wells. It needs a check to be done of Yaxley parish register to find Robert's baptism c1800/1 to find out who his parents were. This information can only come from Huntingdon Records Office as mentioned above
Regards
David, also living so far away in France