Washing a musalla that was touched by a shoe

Q: My mother uses a sandle which she takes to the toilet also. A few times she accidentally stepped on my musallah. I touched the part and it was not wet. With my hand only, I clean the dust without using any water as I am not sure where she exactly stepped on. She also stepped on the musallah with her shoe which she wears when she goes outside. Do I have to wash the musallah? I am currently reading salaah on the same musallah. I have doubts about another musallahs because my nephew urinated on them and the house worker washed them. I dont know if she washed it thrice or not. Can I read salaah on them as she used a detergent?

Repenting from homosexuality

Q: My best friend commited a major sin, he committed homosexuality. I told him that it’s a very big sin and Allah punished the people of Lut (alaihis salaam) for this sin. I told him that he needs to repent and turn back to Allah. My question is, does Allah forgive homosexuality?

Informing one's in-laws about one's past

Q: I have been married for a few years and have children. When the wedding talk was happening, my in laws to be were told that my dad married twice and has children with both wives. They reacted negatively and almost used this reason to stop the talk. Due to their negative reaction, I didn't disclose that my mother was married before and has two children from her previous marriage. But after the wedding I only told my husband. Now, I'm scared of telling my in laws as they are very old fashioned and traditional. I am still in contact with my half-siblings (I'm sure their feeling are hurt by this). What is the Islamic ruling in this situation. I have no secrets from my husband.