Can I be sued. ?

Yes, stop immediately. I would not say anything further on Facebook.

How can I start the process of filing a claim against HUD, the public housing authority, and the section 8 property owner?

This is a very complex issue. I would recommend you speak with an attorney.

Yes, you can sue the company. However, to win the case in court you will have to show that the companies negligence caused your injury.

What are my chances of winning a slip and fall lawsuit against a Hilton hotel?

No two cases are the same. A great deal of the outcome will depend on how significant your injuries were and what the appropriate Connecticut laws...