Are there any regulations to recite Deshika Stotras? While we recite Paduka Sahasram Paddhati based on the star, should this apply to other Deshika Stotras?

There are no particular regulations to recite Deshika Stotras. One can follow the practice of the temples that recite the stotras.
The paddhati based on stars are for some convenience but these are not regulations. We have regulated these for some fruits. Some recite Sristuti on Fridays and Sudarshana Ashtakam on Saturdays, but these are not rules.