Is the reward for reciting adhkar after prayer different whether they are recited in the mosque or while walking back home? And does the hadith, "A servant remains in prayer as long as he is in his place of prayer, awaiting the prayer..." include sitting after prayer?

Reciting the Qur'an in the mosque is superior. It appears that the hadith "as long as he remains in his prayer-place where he prayed" does not include someone who sits remembering Allah and is not awaiting prayer. Imam Bukhari titled a chapter regarding this hadith: "Chapter: One who sits in the mosque awaiting prayer." The reward mentioned in the hadith is contingent upon sitting to await prayer, not merely sitting after prayer for remembrance or i'tikaf, even though there is great reward in that. Regular presence in the mosque atones for sins, involves striving against the self and opposing its desires, and is considered among the best forms of patience and jihad.