Shalom, I am planning to rent my appartment (it should be mentioned at this point that I am renting this appartment myself from a goyishe owner) for an open period of time to another Jew. What halachic principles do I have to consider in this case? Do I need a special rental contract based on din torah? I am specially thinking of possible damages in the appartment (eg interior, furniture, etc.).
Issues of damages do not generally raise halachic concerns, and it is fine to add a clause that the tenant is responsible to pay for/fix all damages. However, fines for late payments can be a cause for concern, depending on how they are expressed in the contract.
To ensure that ribis issues are taken care of, it is customary to add a clause stating that all interest-related payments should are subject to a heter iska, referring to a reliable heter iska (in Israel, many contracts refer to a heter iska of one of the banks, such as the heter iska of Bank Hapoalim).
It is better to ensure that there are no ribis issues, by consulting with a rabbinic authority concerning how fines for late payments should be arrranged.