Mafia 101. Disputed Island

I would like to clarify: are Jen Li and Zero's ultimates available on the fifth night and after, or only on the fifth night? If it's the second option, then if Zero is blocked or isolated on that night, does he lose his ultimate? Is the Hunter's ultimate available on any night except the fifth?
It would be funny if I get the Night Hunter again for the second game in a row.)

- Trap. Digs a pit in front of the target's house. If, subsequently, a killer goes to the target, they fall into the pit, and the assassination attempt fails.

Does it only work with physical attacks, or also with psychic attacks and infections?