There are different methods for basement waterproofing. And if you do it, you should really waterproof completely, otherwise you only cause new problems. But I wouldn’t do it.
I would clarify the issue with the possible drain. Where water comes in, it can also go out. Keyword: hydrostatic pressure during backflow. We also have a drain in the floor in the laundry room in the basement; after several heavy rains, water was pushed up a few centimeters there, and it drained away quickly again. But: if a pipe goes out there and it is not tight, and maybe there is also a (rain) water pipe running on the outside wall, that could be an indication of the damaged spot. All without guarantee, just a thought. If the neighboring house is there, also consider problems caused by the neighbor’s house.
On the subject of ventilation: continuous ventilation at -10°C will probably cause you more mold rather than less. The motto is shock ventilation, also in the basement. At transitional temperatures, you can ventilate longer; in summer and winter, it’s basically just shock ventilation. At least that’s my information, and that’s how I do it too.