Based on the fact that the bottom part of this pipe is wrapped up like a mummy --I'm assuming this is their unfortunate solution trying to prevent some existing leaking there.

I've done some DIY, plumbing and copper work, so I'm not afraid of that. However, based on your description in the picture, and knowing that big problems can come from water leaks, if it were me, it would be worth it to me to just call a plumber.