Is the communal recitation of Surat Yasin specifically on Thursdays, and repeating it as many times as possible for the sake of Palestine, a sound and legitimate act in Islamic law?

Reciting Surat Ya-Sin with the intention of victory for the people of Palestine or other Muslim lands is an innovation (bid'ah), as there is no evidence for it, and because the circulated hadith (definition) "Ya-Sin is for what it is recited for" is false and fabricated.

What is better is to supplicate for their victory and salvation from their enemies, and this is best done during prayer. If a calamity befalls Muslims, it is legislated to perform Qunut (a special supplication) in the five prayers.

Indeed, supplication is the weapon of the believer in times of distress and important matters.