I remember, before my interest for space became complete, seeing huge billboards with the space suited White outside during his spacewalk. No face behind the visor, just the courageous white knight exploring the unknown, far above us! That was impressive!

Yes it was:

I don't know about the atmospheric pressure and composition of Big Gemini, either. Between eventually discovering the dangers of pure oxygen, and, as you mention, the need for compatibility with long-duration, more familiar mixes, the cabin no doubt would have evolved over time away from pure oxy.

Ah, the what-ifs...Gemini was considered entirely an experimental program, and perhaps NASA didn't recognize that it had succeeded in producing an operational, production-ready spacecraft (of what we might call the "Soyuz class"). Imagine, in an alternate universe, Gemini and Apollo executed in parallel instead of sequentially: Gemini the basis of utility vehicles for Earth orbit as far as geosync, Apollo the prototype of deep-space exploration vehicles. Apollo (in our universe) was burdened with compromises to allow it to be a utility vehicle for the Applications program, and I think that in the other universe Apollo as a pure exploratory/long-duration vessel would have turned out rather differently.

--Robert