How to practice religious penances such as Chatrayam, Prajapatyam, etc, which are prescribed by the dharma shastras? Are the practical possibilities for present times?

These types of penances are not possible to practice these days. Instead, one is advised to chant “kRcchra pratinidhi yat kincit hiraNya dhAnam” and donate money. And many do so based on the advice of the respective family priests. It is enough to do this.