I'm not quite sure why he's so fussy constantly. My mom thinks he's gassy. She was holding him upright just now and he had a big burp - so maybe it was just waiting to come up. I never can seem to get him to easily burp either.
And he always seems to want to eat and just cries and cries otherwise. He's also a kicker/puncher so he'll kick and take swings A LOT (and his nails get sharp). He just seems like such an angry child...
Ah, the learning curve. Their nails grow fast, and are really fine, thus they are sharp. Trim them often (weekly, maybe), so he isn't scratching himself, or you. Mitts or socks over his hands is another old fashioned option, but they can come off, especially if he's a feisty one. I often trimmed the babies' nails while they were quiet, which meant while BFing (yeah, that took a while to manage).
As another poster mentioned, the arm flailing is really just due to the immaturity of his nervous system and lack of control over his body. You could try wrapping him tightly in a receiving blanket like the hospital did - many babies prefer being swaddled. He's spent 9 months in tight quarters, and now the big wide world is unfamiliar. Try it to see if baby prefers it, drop it if he doesn't.
Crying is the only way he has to communicate at this point, and he probably only knows that he is somehow uncomfortable: hungry, tummy ache, cold, hot, wet, cranky tired, whatever. It is really frustrating (on both sides) when we as parents can't figure out what is wrong. Relax, talk in soothing tones, and work your way thru the likely reasons (diaper check, assess temp, burp, food, etc). Babies can pick up on our strong emotions, and work themselves into a frenzy beyond the original complaint, so stay as calm as you can, and pass off the baby to another helper as needed to maintain your own sanity.
Re: eating all the time - newborns are growing at an amazing rate, and still developing. They really need to eat nearly round the clock early on - tiny little tummies don't hold much and need refilling often, and mom's milk supply needs to ramp up from zero! It doesn't stay this way forever; baby will grow bigger, supply should match (in a perfect world), baby can get a bigger meal at a time and nurse less often plus hopefully sleep longer between meals.
Hang in there, it gets better!