Ruling on combining prayers in a marketplace due to heavy rain, knowing that some people performing prayers are customers?

What should one who forgot to offer the second Sajda during congregational prayer, and remembered it before the end of the prayer do?

All perfect praise be to Allah, The Lord of The Worlds.                                                                                                                                                          Whoever forgets a pillar of prayer while in congregation must follow the lead of the Imam, and after the latter offers Tasleem, he should offer one Rakah, then perform Sujood As-Sahw (prostration of forgetfulness). And Allah Knows Best.

Is it permissible to make up missed prayers at the times in which praying is disliked?

All perfect praise be to Allah,The Lord of The Worlds                                                                                                                                                                        It is permissible to make up missed prayers at any time even that in which praying is disliked. Absolute supererogatory prayer is forbidden to be performed at the times in which praying is disliked, and this also applies to Ihram and Istikhara prayers. However, there is no harm in offering prayers in Mekah during those times. And Allah Knows Best.

Is washing the private part after urinating (Istinjaa`) a condition, and is it done with water and soap, or with water only?

Istinjaa` is obligatory for removing impurity, and it can be done with toilet paper, or a stone, or water. It is preferable to do Istinjaa` first with paper, or stone, or the like, then to wash the private part with water until making sure that the impurity has been removed. Using soap is not a condition, but there is no harm in doing so provided that it is washed off with water. It is also permissible to use either water, or paper if impurity is removed by any.