Can Paduka Sahasram be recited in the evenings or at night times? Can Paduka Aradhanam be performed at these times?

Paduka Sahasram stotram can be recited any time. Paduka Aradhanam is similar to Perumal Tiruvaradhanam that is done during day times with prescribed requirements such as maintaining cleanliness, etc. to be followed. Generally, state of purity from daytime might not continue to the evening times. Paduka Aradhanam is usually performed during daytimes and not done in the evenings.