Is it permissible to leave immediately after concluding the prayer, or is it better to remain steadfast in order to perform the morning and evening remembrances and those after the prayers, and is steadfastness in performing them in accordance with the Sunnah?

The prescribed remembrances (adhkar) after obligatory prayers do not have to be recited at the prayer rug (musalla). If a person leaves their prayer place and recites them on their way, they have still followed the Sunnah. Similarly, the morning and evening remembrances do not have to be recited at one's prayer place.