As my colleagues indicated, it depends on the type of petition and the nature of the error. If you are pro se and facing dismissal of an otherwise valid claim, you should consider engaging an attorney to clean up the potentially fatal errors.
In addition to the liability concerns stated by Mr. Adams, you don't indicate the extent or severity of your injury. If the injury is minor or temporary, you may have difficulty finding an attorney to handle the matter even if you can establish fault. A important question is whether or nor this was a private walkway or a municipal sidewalk. If the latter, you only have a short time to file a notice of claim with (I am assuming) New York City. You should really consult with an attorney as...
I assume you have an attorney handling this matter. Each case is different and it's quite possible that a case like this could go to trial. If you have trust in your lawyer, then these are questions that he or she should be addressing. If you don't have trust, consider a change.
It's definitely not too late. Report it to the building super, property manager or landlord. Request the contact information for the buildings insurance company. If you are unable to obtain same directly from the building's representatives, the NYC Buildings Department may have the information, particularly if you are living in a multi-unit dwelling.
Even assuming you can make out the basic elements of such a claim, has your emotional distress been documented? Without medical support for your damages, it doesn't really matter how egregious your roommates conduct may have been.
Generally speaking, the answer is no. As a practical matter, what you ask for and what you are entitled to in compensation are usually two different things. Before wasting time and money, consult with an attorney in your area to determine if you have a viable claim and what its value might be.
You are free to consult with and hire personal counsel if there is a real chance the plaintiff will be able to obtain an excess verdict. No one can give an opinion based on the information provided. Get a copy of the bill of particulars from your assigned counsel and then go about looking for a personal attorney to advise you on asset protection.
There are entire lectures and symposium's on the questions you pose. Assuming you have an attorney, sit down with him or her to discuss them. Even if an attorney on this site wanted to venture an opinion on value, there is not enough information to do so. If you don't have an attorney, get one.