Q. Do you think I am able to not claim him and he does not pay NJ taxes?
A. At age 24, he can no longer be a Qualifying Child. So, you no longer have to make that choice. Yo can do both. You can claim him as a Qualifying relative dependent, regardless of whether he files a NJ return. You can only claim him under the qualifying relative (QR) rules. It that case, for being a dependent, it doesn't matter where he lives. If you provide more than half his support, for the year (the 5 month rule is irrelevant), and he has less than $5200 income, you can claim him as a qualifying relative.
For whether he has to file a NJ return, it doesn't matter if you claim him as a dependent. It only matters where he is a resident. Based on the fact that he has made no effort to become a FL resident (get a FL drivers license etc), he is most likely still a NJ resident and needs to file a NJ resident return. But there may still be time to change that. On the other hand, the state tax on $2000 (after exemption) doesn't sound like enough to jump through hoops for (and probably doesn't even meet the filing requirement).
https://www.nj.gov/treasury/taxation/njit23.shtml
Q. So if I file in NJ for him, will he have to pay UI/DI/FLI as well?
A. I'm not very familiar with NJ rules, but it appears that only the NJ employer is responsible for collecting those taxes and there is nowhere on the NJ form for the employee to pay them, if the employer fails to pay. Furthermore, I doubt that it applies in the case of out of state employers.
