What's the reason for Dec'15 currently being the most actively traded contract, why does Mar'15 have more volume than all preceding contracts and what are the general "rules" (so to speak) for volume shift in GE?
The rule is that there are no rules... Everything depends on what's going on in the world of rates. In general, I wouldn't read too much into it.
There can be an expectation that a "harder" tapering or an actual "tightening" will not occur until ~Dec'15 at the earliest. There's less sense of urgency to hedge aggressively with the earlier dated contracts..... maybe.
Are there any comparable curves to GE (outside Euribor) in terms of liquidity into the future and linearity?
Nothing is like the eurodollars in terms of liquidity, but there are STIRs in pretty much every mkt. Short sterling in GBP, BAs in CAD, IRs (and others) in AUD, etc...