This particular aircraft, D-FWME, since leaving the Spanish AF, has had a really terrible string of bad luck. The aircraft, while still in the Spanish AF (still in stock Buchon form), was used in the movie Battle of Britain. Not too long after, in civilian hands, the aircraft was used in the film Patton, dressed to actually look like a high-back Mustang (from far away!), sporting American markings and a temporary belly scoop. However, the aircraft crashed on take-off while the film was being made. In 1986, having been sold to and restored in the U.S., the aircraft crashed on its very first post-restoration take-off. In really horrible state, the aircraft eventually went to Germany in the 90's, where it was rebuilt into G-4 configuration with a DB605 - an incredible amount of work and sum of money went into the rebuild. The aircraft first flew again in 2004, but was severely damaged (one could say 'totaled') less than a year later, when the landing gear collapsed upon landing, which resulted in a violent groundloop. Following extensive rebuild, the aircraft didn't fly again until 2008. Only two weeks after this, however, on approach to landing the right landing gear wouldn't lock down and a wheels-up landing was required. The damage resulting from this incident was far less significant than the 2005 accident, but again it wasn't until almost a whole year later, in 2009, that the aircraft was flying again. This most recent forced landing appears to have had similar, if not better results than the 2008 wheels-up landing, so we should see the aircraft flying again within a year I would suspect.
Unfortunately for EADS, this means that all three of their 109's are currently out of service - the other two include D-FDME, which currently is having engine issues (and still quite fresh out of repairs from a landing gear collapse a few years back), and D-FMBB, which is in long-term overhaul.
All of EADS 109's originate heavily from Spanish-built Hispano HA-1112-M1L airframes, though D-FDME has parts from an original G-10 and is registered as such.
Speaking of the wood props (as you can see in the photos), they are of the modern-production, and in cases such as these they are the type of prop blades that you want.
Regarding the availability of DB605 engines, they were at one time described as being incredibly rare, but in recent years, and with many other Bf-109G and F variants (mostly originals) under restoration to fly in the future, DB605's have seemed to be coming out of the wood work. There are a few companies that specialize in new-build Bf-109 parts, and a few other companies that specialize in new-build DB605 parts and rebuilding DB605 engines, so there is an industry that is present to directly support the restoration and flying operations of these aircraft for years to come.