Observations which favor some hypotheses over others

That which justifies belief.

Anything that changes the posterior probability of a proposition. E is evidence for or against H if P(H|E) differs from the prior P(H). (It's evidence in favor if the posterior is larger than the prior, and evidence against if it's smaller)

Information that compels a rational agent to prefer one course of action over another.

E is evidence for hypothesis H if the posterior probability P(H|E) differs from the prior P(H).

Whatever is true.

An argument that convinces people to act in a way desired by the one who makes the argument.

It's undefined. "Evidence" cannot be defined, since it is the most fundamental concept, from which all others are defined and justified.

[Unexpanded definition] 5 nouns & a verb meaning variously; a reason for updating belief: an existing body of information: a legal term: a symptom: a phenomenological term: & a verb, to make evident (see Expanded Definition in comments)