Hey Filip:
Nice to hear from you again. The following are some links to various sites, but I strongly suggest to contact NARA in Maryland to acquire the UNIT records, for these would give you the greatest amount of detail. Also the Army Corps of Engineers Office of History and Fort Leonard Wood. All great place. The links to all their info (and more) can be found in the research section:
http://www.6thcorpscombatengineers.com/engforum/index.php?showtopic=23
Various links:
http://www.ww2-airborne.us/units/139/139.html
The following forum has many training images, but in order to see them you have to join. That might be worth it.
http://www.armchairgeneral.com/forums/showthread.php?t=107757
http://castraponere.com/bloodonthetalon/
http://castraponere.com/bloodonthetalon/remembrances-of-our-paratrooper-father/
https://www.1starmy.com/p-139th-airborne-engineer-battalion-patch-79633
http://unitpages.military.com/unitpages/unit.do?id=709107
http://www.usmilitariaforum.com/forums/lofiversion/index.php/t93435.html
You may also want to contact my buddy Howard Huebner, for the 507th was placed with the 17th Airborne in 1944. He may be able to shed a little light for you? I will send his contact info via personal messenger, if you'd like. Let me know.
How's that for a start?
Proud Daughter of Walter (Monday) Poniedzialek
540th Engineer Combat Regiment, 2833rd Bn, H&S Co, 4th Platoon
There's "No Bridge Too Far"