Someone's made you an irresistible offer, eh...
The Aero L-29 Delfin is a Czechoslovak-designed and made advanced trainer (tandem ejection seating) used by all WarPac nations' airforces (except Poland which used an indigenous design, the Iskra) and some others. It was last manufactured over 35 years ago, being replaced by the entirely different L-39. It was reckoned to be a docile and pleasant jet trainer.
1. After 14 years in the reasonably wet and cold Estonian climate (that's mid-Norway and mid-Canada latitude!), I'd say even if the skin shows no serious damage (best examine around seams and fasteners on the underside -- after a jetwash or five!), the airframe has basically had it. If we aren't talking corrosion, we're talking likely structural deformation, infestation (including fuel system!) with mosses, funghi and other flora, bird and rodent damage to controls, electrics and fuel lines, perished rubber fuel tanks, congealed lubricants fit for asphalting your drive, fermented fuel, general whiffy decay and leaks galore.
Basically, then, it's held together by the paint. Except that the L-29 was almost never painted...
2. In view of 1 above, this is theoretical at best... You'll never get her flying!
The Aero factory, now in the Czech Republic, had a deal with Boeing or someone Western, and was marketing a warmed-up L-39 known as the L-59, plus a light ground attacker called the L-159. Not sure, but I have a feeling the whole thing sort-of imploded 4 or 5 years ago 'coz nobody bought the things despite some very gee-whizz Farnborough appearances...
I would think an L-29 factory overhaul in the Czech Rep. would cost an arm and a leg, if it can be done at all after 14 years as a museum candidate. Others in the former WarPac may do it for less (Romania, Bulgaria, Belarus, Ukraine, some ex-USSR nations), but the you-get-what-you-pay-for argument may apply. The type seems to have been withdrawn from use around the 2000 mark.
That "Stage III thing" wouldn't apply to an L-29. It's an airport noise measurement and is only relevant to airliners operating in Western Europe, North America, Japan, Australia and a small handful of other countries.
Pneumatics instead of hyd is fine. Grabby brakes! (Like other early jet trainers the L-29 has no nosewheel steering, so you lurch around by differential braking. Must be fun!) I think the Fokker F.27 and quite a few other small airliners have pneumatics. Dunno about the latest regional jets which appear ideal for them, too.
Might be worth a fiver as a museum exhibit, provided you have a washer woman to bring her up to hygiene standards...