Dear Rabbi: I am currently living with non-Jews (only for a few weeks). Am I allowed to cook on the same stove if I have my own pans etc. I bought everything completely new. Also in regards to the oven: If I turn it on 30 minutes before on a very high heat, am I allowed to use it? Thank you very much for your help.

You can use a non-Kosher stove with your kosher pots and pans. As for the oven, for different Halachic reasons I would recommend in addition to preheating the oven to seal your dishes with aluminum foil before placing in the oven. BTW, just a reminder that even new pots and pans need to be immersed in the Mikveh before used.