Is prayer valid when wearing trousers that cause the worshipper extreme discomfort during prostration and sitting? And why is it forbidden to roll up shirt sleeves during prayer, and must one roll up the bottom of long trousers?

Your prayer in tight clothing is valid and does not need to be repeated, as long as the clothing does not reveal the color of the skin. However, it is preferable to be keen on praying in loose-fitting clothing that does not describe the size of the bones, because many scholars have stated the dislike of praying in tight clothing.

As for the prohibition of rolling up sleeves and the like during prayer, it is due to the Prophet's (peace be upon him) prohibition of a worshiper tucking up hair or clothing.

As for rolling up trousers during prayer for fear of isbal (letting the garment hang below the ankles), its discussion has already passed.