His beak is totally fine...
His diet is fine if his staple is pellets, but it's also good for his GI Tract to give him a very small portion of healthy, low-fat seed-mix as a supplement to the pellets, as their GI Tracts are made to eat seeds, and that's also what their beaks are for naturally, and there is a psychological element to it as well..pellets are great, but they don't exist in nature, so as long as you feed a very small portion of a healthy, low-fat seed mix daily that consists of no sunflower seeds, no nuts, and no dried corn, it's actually good and important for both their physical and psychological health.
As far as fresh veggies and fresh dark, leafy greens, keep trying different ones, there are tons, anything but onions, leeks, chives, or any "watery" lettuces...And Bill's idea is a great one...The other thing that can get them to eat their fresh veggies and greens is to microwave a little egg-white (either real or Egg-Beaters egg-whites), chop-up the cooked egg-whites into very tiny pieces, and mix them in really well with the finely-chopped veggies/greens, so that there are bits of egg-white stuck to the veggies/greens. This tends to work very well to get them to eat the whole thing.