Without exception you should always remove decayed joist ends simply because they act as a sort of reservoir for insect infestation and fungiis. There is no way to adequately treat timbers in situ, at least not for a DIYer
Your sistered joist ends need a minimum of 1 meter overlap (ideally longer) with a minimum of three bolts, secured with square washers and nuts. Between the joist and the repair piece you need to have a star washer on the bolt. Cut ends need to betreated with preservative
There are various techniques for dealing with the ends. An old technique used to be to dip the end in hot tar or bitumen, whilst others favoured (now banned) creosote. On repair works where we've done these in recent years, however, the approach has been to resin anchor bolt a pitch pine or sometimes a pressure treated ledger plate onto the wall and then use joist hangers off that. In areas below ground level where the walls could contain damp and in that instance we often put a layer of DPM between the wall and the back face of the ledger plate to reduce moisture ingress. The reason for using a ledger as opposed to re-inserting timbers into the holes in the wall is two-fold - firtsly the new sistered joist ends don't line-up to the holes, and secondly those sockets in masonry tend to trap moisture and start off rot far earlier
