Is it permissible to perform Salah for the deceased, or is it limited to supplication, charity, and fasting on their behalf? And is what is practiced in some Arab countries and called "Al-Shadir" – reciting the Quran in public roads – considered an innovation, and why?

Prayer for the soul of the deceased is impermissible, because the fundamental principle is that no one prays on behalf of another, and none of the scholars have allowed that. We advise what is prescribed by Sharia, such as supplication (Du'a), charity (Sadaqah), fasting on their behalf if they had an obligatory fast due, and performing Hajj on their behalf if they had an obligatory Hajj due, based on legitimate Sharia evidence. As for setting up marquees (tents) in public roads to recite the Quran for the soul of the deceased, it is an innovation (Bid'ah) and a newly invented matter that has no basis in Sharia, and it is rejected for its doer, along with the Sharia violations that often accompany it.