Can a black hole turn back into a star? I understand that a black hole happens after a star exhaustions elements capable of undergoing fusion.  Without the energy produced by fusion the remaining mass of the star collapses on itself and forms a black hole.  I conclude black holes must be deficient in hydrogen, helium and elements that undergo fusion in stars.  I understand that hydrogen and the like undergoes fusion in stars in part (or completely?) because of the gravitational pressure which occurs in stars.

Suppose a young star replete with hydrogen merged with a black hole.  My question: would the result be a larger black hole, or a radiant star with a very massive heart?  Could a massive infusion of (fusible?) elements reboot the black hole back into a star?
No.

A black hole is characterised by the formation of an event horizon. Matter which travels past an event horizon cannot return to the space outside the event horizon, to do so would require the matter to travel faster than light, and so would require infinite energy. 

There is nothing like a regular star "inside" a black hole. The general relativity model of a black hole contains a singularity. Matter which enters a black hole is certain to reach this singularity in a (usually short) amount of time. Adding hydrogen to a black hole would just make the black hole more massive. There is a theorem in mathematical physics that the only properties that a black hole can have are mass, angular momentum and charge. In other words, a black hole made of collapsed hydrogen would be identical to one made of collapsed iron. There is no matter in a black hole, only mass.

The formation of a black hole normally occurs when a core in a massive star has a certain amount of iron, which saps the core of energy causing collapse. If the resulting object has more than about 3 solar masses, then nothing in the universe can stop it from collapsing all the way to a singularity.

As with much about general relativity, your intuition is a very bad guide to how black holes work. However General relativity is a very good model for how black holes should form and behave