Well I guess anything is possible. If the copper lines/fittings are corroded there could be a bad connection with the hose no matter how tight you have the clamps.
Letting it drip and run down to the bottom.
Without the stuff in the engine bay mentioned above there's 3 options:
- inlet leaking...
No don't pour that into your cooling system. Might be a band aid fix for short term but wouldn't use it here
Just remove it for now and get it looked at
Yep leaking heater core, remove and inspect. A local radiator shop might be able to fix or find a good one in the classifieds.
While it's out you can pressure test it to be sure.
I'd bypass it in the engine bay for now