Does saying: "O Allah, grant me a visit to Mecca" or "O Allah, I find constriction in my chest, so expand my chest for me" during prostration invalidate the prayer?

The prayer is not invalidated by the aforementioned supplication. Scholars have differed on the permissibility of a worshiper supplicating for worldly pleasures during prayer. Some, like the Hanbalis, believe that such a supplication invalidates the prayer, while others permit supplicating for whatever one wishes of the good of this world and the hereafter, citing the hadith (definition) of Ibn Mas'ud: "Then let him choose whatever supplication he likes most." Supplicating for matters related to the hereafter is preferable.