Louis. a löt of questions, but not easy to answer.
• Who developped the side safety that was not visible on the initial actions, and from which year dates back this development ?
No exact date known, but a 1920s ad by Max Heym shows it.
• When did the 1880 patent expired ?
As the Heeren DRP # 13250 was applied for on July 11, 1880, it was in the public domain 20 years later, July 12, 1900
• Until when was the Heeren trademark protected ?
1945
• Where post-WW2 Glaser Heeren actions manufactured by Omega in Switzerland standard Heeren actions or was the mechanism modified by Glaser ?
Not the internal mechanism, but the Omega actions are longer, that is, the "receiver ring" is 30 mm instead of the Suhl 18 mm.
• Who - apart maybe, Hartmann & Weiss and the Ferlach guntrade, manufactures Heeren actions nowadays ?
I don't know, but post-WW2 makers were Orea and Furtschegger too, besides Outschar. They made xhanges, F.i. coil- instead of leaf springs. Outschar slghtly slanted the breechblock by about 3 degrees to prevent the infamous binding at pressures over 3000 bar.
• Heeren rifles were to my knowledge originally available in 6,5 , 7 and 8 mm European calibres mostly (and by extension now in their US equivalent) but not in bigger calibres such as 9,3 (or US equivalent nowadays). Should this mean that the Heeren falling block action is not adapted to them ?

There is no earthly reason why a Heeren action rifle could not be built in 9.3x74R or .450-400. But Heeren rifles were usually meant as short, light stalking rifles for Alpine mountain use on roe, chamois and red deer. Medium or large bores are less suited for such use. Yes, I have once seen a Heeren rifle in 10.3x60R, a nitro load of the .450-400 2 3/8" Express. Hunting law of the Swiss canton Graubünden/Grischun prescribes single shot rifles so chambered.