Shelf life of open jarred anchovies and anchovy paste in the fridge?
I would assume there is enough salt content to render these fairly stable in the fridge.  I would just avoid fingers in the jar to avoid any potential surface contamination.  In the long run, I would go with whole, salted anchovy, which have an indefinite shelf life.  I keep an 800 gram can (opened, but covered with foil) in the fridge, using one or two anchovies at a time.  It lasts me 8 - 12 months easily.