Is there a universal (general) definition of gerund, infinitive and participle applicable to all languages despite the differences between them?
"Participle" can be defined pretty reliably as "an inflected form of a verb that acts as an adjective". But the line between a participle and any other adjective derived from a verb is fairly arbitrary: there's no obvious descriptive reason why -tus adjectives in Latin are "participles" and -τος adjectives in Greek are not. It just comes down to grammatical tradition.
"Gerund" and "infinitive" are even harder. They're both labels for "a form of a verb that acts as a noun". But the decision to call Latin amāndum and English going "gerunds", and Latin amāre and English to go "infinitives", is also fairly arbitrary. You can argue that Latin and English infinitives mark voice and sometimes aspect while gerunds don't, but there are plenty of other languages where infinitives don't mark those things—off the top of my head, Egyptian and Akkadian. Once again, the distinction mostly comes down to grammatical tradition.
Universal dependencies is trying to to that and their attempt on defining some non-finite verb forms in a language-independent way can be seen here. It is still very much informed by Indogermanic languages and has a strong language family bias for that reason.