Can I assume a mortgage even though I filed Chapter 13 and I'm still paying on it?
Very likely not.
First and foremost, if you are still paying on the plan, you are still subject to it. That means that you cannot add significant new obligations--such as assuming a mortgage--which will impact on your ability to pay as per the plan, at least without bankrutpcy trustee approval. You can seek that approval, but it's unlikely you'll get; you should also ask yourself whether it's wise to add a new obligation, when you are still subject to the obligations in the plan.
Second, you would need bank approval to assume the mortgage, and that approval is very unlikely to be granted. You under Chapter 13; you are, without any insult being meant, not a good credit risk. Why would a bank allow the current obligee out from under it's obligation to substitute someone who is still under a bankruptcy plan?