1) that seems to go away with usage. I wish HiFiMan would simply work these out a bit before they send them out, but, they don't so some are stiff until you use them a bit. I agree it's annoying, but it does seem to go away. Mine were never that stiff, but they do swivel much more easily now than when I first got them.
2) Yes, the grills will move. HiFiMan makes it so that they are easily replaceable/moddable. Them moving a bit is sort of the tradeoff there. They're only held on by that tiny plastic ring. You can feel free to super glue them in place if it bothers you, but it doesn't cause any issue other than "feeling off"
3) Hmm, yeah, the HE400i is a *strange* headphone to amp, as some lower powered amps are fine with it, and some medium power amps have trouble with it. It is ****extremely*** current hungry, so it tends to work best with lower output impedance amps, and amps that use current feedback regulation (as opposed to voltage feedback).
An example of this is that I could never adequately power my HD650 with my iPhone, yet I can power the HE400i perfectly fine with my iPhone. But in reverse, the AudioEngine D1 powered my HD650 perfectly adequately, but struggled to power the HE400i, becoming a muddled mess when I pushed it past quiet volumes.