On the F-27 if one propeller has been feathered, either automatically or manually, the auto-feather function of the other engine is disabled. The other engine can be manually feathered, but why anyone would want to do that before relighting the first engine would be a mystery. There is no quick relight feature, indeed the unfeathering action alone takes five seconds or so.
The fuel system is essentially gravity feed. Fuel from the main tanks is supplied to a collector tank in each nacelle and from there to the engine fuel lines via two low pressure pumps located in the collector tank. They would normally be on for take-off, but the engine would still operate without them being on.