Silicon-based life?

Non-starter. Silicon-silicon bond is far too weak & silicon-hydrogen bond is very weak: silanes hydrolyze in water.


Or to really think outside the box, what about plasma-based life some
have speculated could live inside stars?

No. There are no nuclear structures analogous to chemical bonds. Such structures are essential for life.


I too have the feeling that most beings made in this Universe will be
variations of life on Earth at least in terms of basic makeup, but if
organisms can form inside what we consider extreme environments,
might they also have to be made of different stuff by necessity?

They will be made of exactly the same stuff, by necessity.

David F Mayer