Is one allowed to sue a shul (that is a corporation) when they were negligent and somebody was severely injured? (And when the shul is insured?) Also, what if one generally plans to settle out of court, but files the suit as part of the process to settle out of court.
Suing a Shul should be only in a rabbinical court (according to the Shulchan Aruch Choshen Mishpat 26, 1). If the insurance company is of gentiles, in principle, they should also be sued only in a rabbinical court, because the Torah prohibition of Initiating Litigation in a Civil Court is even when a Jew is dealing with a gentile (Responsa Tashbetz part 2, 290 from a Midrash Yelamdeinu - Tanchuma on the beginning of Shoftim - Judges) . Nevertheless, if it is clear that they will not agree to litigate according to Torah law but only in a civil court, one is allowed to sue them in a civil court (according to the Shulchan Aruch Choshen Mishpat 26, 2). Also in such a case it is preferable to offer them to litigate in a rabbinical court and only after they refuse, turn to civil court. In a case where it is permitted to file a claim in a civil court, it is permitted to do so also as part of the tactics of reaching a settlement out of court.