- He is quite disrespectful towards other employees
This is pretty common. When someone moves from a more casual workplace to a more formal one (or from no workplace at all, e.g. university), they don't necessarily understand what is considered disrespectful in the new context. If they're arrogant or unobservant then they won't pick up fast on what's rubbing people the wrong way. Yeah, yeah, "it should be obvious", "what he's saying is clearly inappropriate", all of that. What's obvious to you may not be obvious to him.
Somebody with authority over him needs to assess what he's doing. If it's not acceptable they need to inform him how he must change. If it is acceptable they need to inform you how you must change (stop interpreting it as disrespect). So yes, you should bring this to your manager, with clear examples of what you think is problematic.
Merely the fact that something is unfamiliar or weird to you is usually not a good reason to forbid your colleagues from doing it. I'd keep quiet on this one, because in combination with your other complaints you don't want to make it look as if you're also trying to enforce your personal and subjective view of what's normal.
If he's "acting out", that is doing weird things solely to get attention, then that's a more concrete complaint. Firstly he's distracting the office, which is bad. Secondly there's probably some issue that's the root cause of why he feels he needs attention, so it's his manager's job to either get to the bottom of that (maybe he needs more support than he's getting) or else decide that it's not in the organisation's interest to try to solve it (maybe he needs more support than the organisation is prepared to give).
- is entitled and has a huge ego
Having a huge ego usually isn't in itself an infraction. You need specific things that he does because of his ego, and that are infractions. For example, if he fails to follow instructions given to him by more experienced colleagues because he thinks he knows better, and he gets it wrong. Then raise with your manager the fact that he chose not to follow the instructions. Don't raise the fact that in your opinion he has an excessive ego.
Unfortunately, raising this kind of thing requires a period of evidence-gathering, and that requires contact. Therefore, approach the co-operation with the plan that you will mentor him, and part of the way you'll do that is to figure out exactly what he's doing wrong, and escalate those things to someone who has authority to tell him that his "excuses" are no good. And if that doesn't work, to go through the process to fire him.
- normally I would just ignore such a colleague
For the sake of your own professional development, it would benefit you to work on this. You will encounter people who are arrogant, rude, weird, annoying or (in this case) all four. If you can do better than just ignoring them then you'll be a more effective employee because you have a new skill/ability that you don't have currently. If you trust your manager with the knowledge that this person aggravates you even beyond their concrete infractions, this is another good reason to raise it, since your manager has an interest in your professional development. Then you can come up together with a combined plan to (a) address your colleague's problems that need to be addressed, (b) address your difficulties in dealing with what remains.