Is it a condition for the forty days to be continuous in the forty-day prayer, such that no obligatory prayer is missed during it, or can the number be completed even if some prayers are missed?

If the Hadith intended is: "Whoever prays to Allah for forty days, catching the first takbir, will have two immunities written for him: an immunity from the Fire and an immunity from hypocrisy," then it is a Hasan (good) Hadith. However, the reward associated with it is only attained by performing forty consecutive congregational prayers. If one misses a prayer before completing the forty, they will not attain the reward unless they recommence another forty days. As for the Hadith of Anas: "Whoever prays forty prayers in my mosque, without missing a prayer, will have an immunity from the Fire written for him, salvation from punishment, and will be cleared of hypocrisy," it is Da'if (weak).