I live in an apartment complex. Never mind the Management: treat the matter as if it was a neighborhood. Besides, the complex is a community. You need to report any drug activities to the police, not Management. Many Housing projects owned by a housing authority have their own police department and such activities should be reported to them.
Doubtful, but yu can try. You are probably responsible for pest control in your own unit.
Whether a tenant is disabled does not have a bearing on whether he can be evicted. If a PHA has the right to evict a tenant then it can evict such person regardless of disability.