What is the ruling with regards to running while going for Salah, inside or outside of the Masjid?
Whether inside or outside of the masjid, it is not proper to run towards Salah. One may harm himself while doing so. In fact, one should walk in a composed and relaxed manner, just as it has been ordered in Ahadith.
فی سنن الترمذی: عن ابی ہریرۃ قال قال رسول اللہ ﷺ: اذا اقیمت الصلوٰۃ فلا تأتوہا وأنتم تسعون ولکن إئتوها وأنتم تمشون وعلیکم السکینۃ فما ادرکتم فصلوا وما فاتکم فاتموا۔ اھ (ج۱، ص۴۴) واللہ اعلم بالصواب