Are my prayers valid despite frequent absentmindedness and the thought that I am in another prayer, or saying the Taslim unintentionally, or not feeling the prayer?

You must turn away from misgivings (waswas) and not pay attention to them. So, whoever experiences frequent doubts, to the extent that they occur every day, even if only once, should disregard them and not act upon what they doubt. Your prayer is valid and is not invalidated by doubt during it, nor is prostration of forgetfulness (sujud al-sahw) required of you. Furthermore, according to the majority of scholars, it is not necessary to renew the intention (niyyah) throughout all parts of the prayer.