Is the prayer valid for someone who intended to pray Asr, then doubted during it whether it was Maghrib, so he completed it as three rak'ahs and performed the prostration of forgetfulness (sujud al-sahw)? And is it permissible to delay the prostration of forgetfulness until he remembers it?

If you intended to pray at the beginning of the prayer or a little before it, your prayer is valid, and the forgetfulness of the intention after that does not harm it. If you made the taslim (definition) from the Asr prayer after three rak'ahs, having forgotten, and then remembered, you must perform a fourth rak'ah, followed by the prostrations of forgetfulness (sujud (definition) al-sahw) at the end of the prayer. However, if a long time elapsed between the taslim and remembering the deficiency, you must repeat the entire prayer. As for delaying the prostrations of forgetfulness due to forgetfulness until a long time has passed, the prostrations are dropped, and the prayer is not invalidated. Intentionally omitting the prostrations of forgetfulness is a matter of scholarly disagreement.