Both phenomena are in the "they all do that sir" category. Mine certainly does both and has since I've owned it.
The noise on startup is the ABS testing itself. There's lots of chat on the Discovery Owners' Club Forum (and others - probably on here, in fact) about it.
There's less chat about the "firmer pedal on second press" but I've seen enough on the Discoweb forum (http://www.discoweb.org/forums/forumdisplay.php?f=4) to reassure me that it is common and not worth worrying about. I believe LandRover sorted it at some point, maybe when the Discovery2 was facelifted?