All-nighter in Venice?

Hello,

My boyfriend and I are interrailing and want visit Venice, but can’t afford a night there. Our initial plan was to day-trip but I’ve read that it’ll be so crowded that you won’t feel the atmosphere, so we’ve come up with a plan to do an all-nighter in Venice. We want to arrive late afternoon to take a gondala, eat our packed dinner, spend the night wandering around the city and then get our train back to Bologna in the late-morning.

In order to make this work, I wanted to check:

* Are there free/affordable public toilets? Are they open at night?
* Are there any benches to sit on? If so, where?
* Will there be anything open to do at night? Bars etc.

If this is a terrible idea, let me know!! Thanks :)

All-nighter in Venice?