Ian, the FW 190 was certainly running, although not airworthy. As far as I know, the engine was inhibited after the last engine run, before it went to the IWM, Lambeth.
Grant (Nuumann) can probably reveal more on this one, as he posted a video of its last engine run on the forum a while back.
The Wellington had been serviceable, and airworthy, when it was first earmarked for museum preservation, back in the late 1950's, and appeared at a number of air shows, as a static display, until the early 1960's. But, even if the engines are capable of servicing to operational standard, the airframe would not pass for airworthiness, by today's standards. Once the refurb is complete, I would expect some of the electrics and hydraulics would probably be operational.
The Typhoon of course, is missing all of the cooling system, although the Sabre engine is, I believe, complete. Even if the Conservation Center are able to build a new radiator, ducting, trunking and other ancillaries, and I don't know, as yet, if this is intended, I doubt they'd risk running the engine - they were prone to engine fire on start-up when in service, so a heck of a risk after 70 years !
Regular maintenance is carried out on all the Museum's exhibits. and, for example, I was fortunate enough to have access to the Me410, last year, when it was undergoing such work. Where possible, electrics, hydraulics etc are maintained in working order, but, like any mechanical object, when not used, things like seals can degrade, even if they are newly fitted items, so to pull a particular aircraft from the hangar and start it up, would involve a thorough inspection, and almost certainly the servicing of all systems, and replacement of some parts.