Could International Space Station (hypothetically) harvest air supply from outside the hull?

Assume a) we have infinite energy and infinite cooling b) solid debris that would instantly exterminate any pump is a non-issue, we have ultimate imperishable mega-filter-sponge.

ISS altitude is ~400km above surface. Several sources list pressure up there at 10^-7 mbar. Ultra high vacuum pumps can give -9. But even then, correct me if I'm wrong, in rotating frame of reference tied to Earth's surface, atmosphere at that altitude moves mostly upwards and from equator to poles (convective movement), while ISS is moving laterally at the speed of a bullet shot by a rifle that was shot by another rifle.

a) Could ISS harvest air from its own outer hull, if it was shaped as a collecting nozzle?

b) Could ISS use this harvested air as its own ion thruster propellant, resulting in positive delta-V, kind-of like a battery-powered plane drone does (again, assume our solar panels are ultra-perfect and infinitely powerful and reliable, and we have ultra-radiator to remove excess heat with no problem)?

c) If its hull was shaped as a collecting nozzle, could this be achieved with a general-purpose industrial pump (vacuum quality ~1 mbar), or do we need a turbopump anyway?

d) Is this air (at 400km altitude, composition-wise) breathable?

e) How harder would the task get if assumption A's parts, or one of them, are removed (infinite energy / infinite cooling)?

Bonus points if all Mel Brooks' Mega Maid jokes go under one comment. It's okay, I love that film too.