Yes, it will read USB OTG just fine. That's how I transferred my music and backups from my old 64 GB MicroSDXC.
The buttons disappear when watching videos but I don't know the answers to your others. Someone mentioned an app that gives better control over the menu buttons. Requires root, which is easy too.
Sent from a van down by the river using my AT&T LG G2 and Tapatalk 4.
Nexus 5 32GB
HTC Droid DNA
LG G2, Samsung Galaxy S4, Samsung Galaxy Note II, Samsung Galaxy SIII, HTC One S, Toshiba Thrive Tablet, Samsung Galaxy Note, Samsung Galaxy SII, LG G2X, MyTouch 4G Slide, iPhone 4s, MyTouch 4G, iPhone 3GS, Some Blackberries, HTC Diamond Touch, HTC Mogul, HTC PC6700, handful of Nokias... all the way back to the original Motorola MicroTAC in 1994.