Is there a definition of "sentence" that is applicable to all languages?
A word or set of grammatically linked words expressing a complete thought.
"Expressing a complete thought" is context-dependent: "Sure" might or might not be a sentence. It is as an answer to, "Care for some coffee?" but not as part of "Don't be so sure".
The context needn't be conversational: "INT. DAY" is a sentence, in the context of a movie script.
I agree with the comments - it would help if you narrowed down the perspective from which you look on the topic. My primary approach would be actually top-down definition, i.e. sentence as a constitutive element of an utterance.
Utterance - a unit of speech typically with silence on the part of a speaker as boundaries.
Sentence - a unit constituting an utterance and intended to correspond to a meaningful complex structuring an idea, determined on many different levels requiring to structure one's speech into finite units due to our physiological and cognitive limitations.
Syntactic clause/phrase or Speech clause - depending further on perspective assumed a constitutive unit of sentence.
I take a sentence to be declarative, hence questions are not sentences, but, if you like, interrogative phrases, and imperatives are similarly not sentences either, but, if you like, commanding phrases. The standard semantics for questions and imperatives are based on truth-coditional models, but the original question I attempted to address was not about that.