You could still have a chance with some departments. My department probably would not hire you right now. However, that does not mean that the two agencies you're applying for will not. Having been fired from one job due to leaving for a family emergency would not be such a concern depending on how long ago it was and what the emergency was. Hopefully for your other "departures", you gave a two week notice. Having carried a concealed firearm illegally a few years ago would cause concern. If your accounts are not currently delinquent, and you've been making payments on time for a while, and you don't owe too much money, then I wouldn't worry too much about that. Under the table work is not so unusual. Having bounced a few checks, if not recently, probably wouldn't hurt you too much in and of itself. Having illegal cable would also cause concern.
I would suggest proceeding. It probably can't hurt. If you are not hired, you might be able to find out why. 27 is still relatively young. Continue to do the right things. Whatever job you have or get, even if it is not one your dream job, be a good employee. Your work history can be important when trying to get another job. Keep paying your bills on time, and your credit history will improve. If you don't get hired now, maybe you will in a few years.
It is very good that you have never used drugs. I commend you for that. Having used drugs is a hurdle for many people that want to be police officers.