Yes, water the mandevilla...whatever you do,don't let it dry out. But don't waterlog it either. Just keep an eye out that it doesn't dry out completely and that the soil stays a little moist. Good luck!
And yes, try to keep it going as long as you can in a sunny room for the winter if that's all you can do. It will drop leaves and you will get some die back, but as above, don't let it dry out completely between waterings. Good luck!