There are other theoretical biochemistry possibilities[1]. Silicon, for example, works well in low-pressure environments. It's an immense stretch of the imagination to think about life-forms that use semiconductors to do useful work, but is certainly a fun thought experiment.

[1]: https://en.wikipedia.org/wiki/Hypothetical_types_of_biochemi...

Yes, it's possible, just less likely. How much less likely is hard to tell, but I if you hear hoofsteps, you first think of horses, not zebras.

It may not be based on elemental matter, or matter at all.

Hmm, true. But then, interaction with elemental matter life forms (like us) would become terribly difficult; it might be hard to even notice there's a life form existing in anti-matter.

Do you think the periodic table contains all the elements in the universe?

Yes, since from what I understand, any heavier elements would be so unstable they wouldn't last a billionth of a second.

That's the general assumption, even though there might be another stable "island" of fairly stable isotopes for higher-order elements than observed so far. But as I said, they'd need to be created first through nuclear fusion of lower elements, so their existence is obviously less likely, let alone life forms evolving on top of them.