Tool training

Peace and happy holidays to Rabbi Michi
I have a few questions regarding the kosher nature of the dishes. It should be noted that I live in a house where I am the only one who keeps kosher and the rest are secular.
I would be happy if you could answer me in detail any questions and any advice or tips for the situation I am in.

1. If I heated up food in the oven and microwave that I had already prepared that was prepared with dishes that were not prepared but had only been put through the dishwasher (secular family members who came to clean up), do I need to prepare the oven and microwave again? If the stove was not used, but things were placed on it from time to time, what is the ruling regarding them?

2. If non-kosher utensils are placed in the place where I keep utensils that I have certified (they were certified, but then they were used for food that is kosher, although I trust it, but was prepared in non-kosher utensils), what is the ruling regarding the utensils that I have certified?
Do they need to be sterilized or is it enough to wash with soap? It should be noted that I don’t know what utensils they used and put in my pile of kosher utensils.

Thank you very much in advance.