Is it permissible for someone who enters the mosque while they are praying 'Isha with the intention of combining prayers to join them with the intention of praying Maghrib, or should he pray Maghrib individually and then join the congregation if they have not finished? And is it permissible for neighbors of the mosque who live very close (30 meters or less) to abandon combining prayers during rain and cold on the pretext of their proximity?

It is permissible for someone who intends to pray Maghrib to join a congregation praying 'Isha, as the difference in intention between the follower and the Imam does not affect it. Combining prayers due to rain is permissible because of hardship, but it is not obligatory. So, there is no sin on someone whose home is close to the mosque and who chooses not to combine prayers. Indeed, some scholars have stated the impermissibility of combining prayers in this situation.