Clunky changes: Fazers are clunky anyway, and it takes practice to make smooth changes anyhow. It's one of those things where an instructor can advise - but the only way to learn smooth changes, is to do it (take your time changing gear if need be). If your bike hasn't had it, an oil change can take some of the clunkiness out.
Going down multiple gears isn't a problem, it's matching engine speed / road speed, so as not to make the bike lurch: in fact IIRC, block changing is almost a must for advanced tests. Again it's a practice thing.
Cornering: if you've just come off a 125, bear in mind a big bike (and especially a new-to-you, unfamiliar bike) will handle differently; your tyres will have likely more grip than you give them credit for. Part of it is the "look where you want to go, and you'll end up there", part of it is making sure you're sufficiently relaxed on the bike (almost letting the bike "do it's own thing") - if you're tense, you can end up "fighting" with the bike. Try one of those off-road training days (BMW and I think Honda run these, amongst others) - it'll give you a feel for the bike sliding about, and if (when) it happens on the road (fuel, gravel, grain etc) you won't be so inclined to panic.
Speed: it takes time to get used to windblast (and indeed, noise) on a bike (M-ways are even worse), ultimately speed comes from being smooth, and smoothness comes from looking ahead and giving yourself a chance to plan things through.