What is the ruling on combining prayers at the Musala (Place for prayer) of a shopping center because of heavy rain, knowing that some people come from outside that center?

Praise be to Allah, the Lord of the Worlds.

If there is hardship in going back to that Musala at the time of Asr or Isha` prayers, then it is permissible to combine prayers in twos only (Duhr with Asr and Maghrib with Isha`). Kindly consider calling us. And Allah Knows Best.

Is it permissible for a woman who has become pure before the end of forty days of confinement to perform different acts of worship? and is it lawful for her husband to have sex with her?

Once postpartum bleeding ceases and she is certain that it won`t happen again, she becomes pure, and so she should perform Ghusl (ritual bath), pray, and fast. She can also have sex with her husband even before the end of (40) days because the minimum of postpartum bleeding is a moment, and the maximum is (60) days. However, the postpartum bleeding for the majority of women is (40) days, but this does not apply to rest of them.

Is it permissible to offer Salah (prayer) on behalf of the sick who is on his/her death bed, and is incapable of offering it?

It`s impermissible to offer Salah on behalf of the sick, or the dead.

Is it permissible for a person who is in a state of Janabah (Ritual impurity) to clip his nails, or to cut his hair?

It is permissible for those in a state of Janabah and menstruation to clip their nails and to shave whatever hair that is permissible to be shaved. And Allah Knows Best.