I too think it sounds like there are training &/or pain issues. Changing the bit(to what?) and using a noseband that forces him to put up with it more will likely only be a temporary help and sorry to say but rearing is most likely due to rider error IME - you're holding him too tight so he has to go up.
I get the idea this is a relatively new horse for you? Especially as he grinds his teeth when out(& I presume you mean throws his head?), is it possible you're asking more than he's ready for? Considering the teeth & head throwing, have you considered/tried him without a bit? It's very possible that it's having a bit in his mouth(due to previous experience or pain, not nec. Current) is the major source of the problems.
On the feed front, yes, if he's getting too many calories generally, &/or starchy/sugary diet, &/or too little roughage, &/or he's imbalanced or deficient in some nutrient(Mg comes to mind as one commonly associated with overly 'nervy' behaviour), it could well be a problem. As others have said, beet pulp is generally a great, low sugar feed, but it is high in calories, so if he's already a good weight... or overgood
, probably not the best. Cereal hay/chaff, such as oaten, can be high in sugar & can also have grains in it, so I'd keep that to a minimum, or if you think he's over sensitive to sugar, soak & drain it to get rid of extra sugar & oats before feeding. Lucerne/alfalfa chaff is another great horse feed generally which is quite low in sugar. It's another that's quite high energy though, so not the best option for 'easy keepers'.
So... without knowing whether your horse is thin, fat, healthy, etc, feed-wise I'd be inclined to feed him a 'normal' healthy diet of hay/grass and a complete supp or (grain/molasses free) 'ration balancer' for his nutrition. If he needs more than this, then you can think about 'hard feeds' for extra energy.