Is it permissible to perform tayammum instead of ghusl for hemodialysis at the hospital due to lack of time, and is it permissible to perform tayammum for Dhuhr prayer and perform ghusl after waking up at Asr time due to exhaustion?

If performing ghusl (definition) (ritual bath) would cause you to be late for the hospital and possibly miss your dialysis appointment, then it is permissible for you to perform tayammum (definition) (dry ablution) for the Fajr prayer, and you are not required to repeat it after you return. As for performing tayammum for the Dhuhr prayer when you are able to perform ghusl, this is not permissible. However, it is permissible for you to combine the Dhuhr and Asr prayers by delaying Dhuhr (jam' ta'khir) if you find difficulty in performing Dhuhr at its prescribed time. In this case, you can delay ghusl until the time of Asr, and then combine the two prayers.