So when scientists talk about evidence of life on Mars, or the possibility of life on other planets, they don’t have a scientific definition for that?

You pounced on their use of the word "life", but of course the question here is "human life", not "life" in general, and that's a term that does not simply mean live human cells, and does not have a straightforward scientific definition the way "life" does (at least, not when used in the sense it's used in the abortion debate).

But life doesn't have a straightforward definion either.

Are viruses alive? What about robots? Or cities? Or earth?

It's a philosophical question and not something that can be decided by experiment.

Definitions are just assumptions and can differ for each paper. They come from convention or philosophy, not science itself.

“Definitions are just assumptions” is pretty tautologically false.

Science at its core aims to define things: hypotheses are proposed and proven/disproven in search of pinning down clearly defined rules and patterns.

Is gravity just an assumption that differs for each of us?

Gravity as you mean it isn't a definition, it's a theory.

If you named it vticarg instead and defined the word "gravity" as loud noises, that would be fine scientifically.

Indeed you will find "gravity" defined different ways in different papers. Sometimes it's Newtonian, sometimes relativity, sometimes MOND.