Will someone who donates a prayer rug or a loudspeaker to the mosque receive a reward for every worshipper's prayer in the mosque?

Your donation to the mosque is among righteous deeds, and it is hoped that it will be an ongoing charity (Sadaqah Jariyah) for you. As for the extent of the reward, that is known only to Allah, and it is not possible to definitively state a specific reward that has not been mentioned in the Sharia. So, give charity and hope for Allah's bounty; for a good deed with Him is multiplied ten times over to many folds.