Q:

Is a fluorine/hydrogen engine feasible for use in space?

Fluorine is a bit more efficient chemically than oxygen. It has never been used as a launcher oxidizer because it and its exhaust products are so toxic. That's as much I've heard about it anyway. But, would it be useful for engines used only in space where toxicity doesn't matter, as in a third stage or for satellite station-keeping in small engines? Or is it too corrosive even for that?

A:

The safety-related costs of developing, testing, and fueling fluorine-oxidized rockets outweigh the costs of building slightly bigger and less efficient rockets using hypergolics or LOX. 
In launcher stages, hydrolox is only 5% less efficient by Isp than hydrogen-fluorine; the higher density of fluorine makes for more compact tankage, though, which means less structural mass overall. Your rocket will wind up bigger using lox, but it will also be cheaper, safer, and less toxic. 
Hydrogen-fluorine also burns about 900 degrees hotter than hydrolox; keeping the chamber and nozzle robust against hot corrosive gases is going to add weight one way or another. 
Fluorine is cryogenic, liquifying at close to the same temperature as oxygen, so it's impractical to store for long-term missions. For long-term satellite stationkeeping, the go-to solution nowadays is an electric propulsion system such as ion thrusters; way more efficient than H/F and again, much safer.

