Would a windmilling engine at cruise (i.e. shut down) still produce some degree of hydraulic pressure and electrical generation? What sort of speed would the engine be rotating at compared to idle?
A windmilling engine can produce some hydraulic pressure - in fact some aircraft can get away without a RAT because in an all-engine out condition there is sufficient hydraulic pressure from the windmilling engines to allow basic aircraft control (the 747-400 (and earlier 747 models) fall into this category - however the 747-8 needs a RAT). However the GE90 on the 777 does not produce much hydraulic pressure when windmilling (big fan, little core means relatively low N2 windmill speeds) - hence the 777 needs a RAT. Some newer installations (e.g. the GEnx) actually disconnect the hydraulic pump for an engine shut-down in flight to increase the windmill N2 sufficiently to make a windmill re-start physically possible.
There is no meaningful electrical generation on most windmilling engines - once N2 (N3) drops below 50%, the IDG drive disconnects.