
So you mean that rubber pipe is good and heater core pipe is leak itself.
You can gas weld it, it will be just like puncture on rubber tube
Are you using heater?
If not disconnect it, it will leak again.
Yes, do paint it. But before paint make sure to scrub all the rust, or it will eat your car from inside.
And it appears that you have just washed engine bay with water, avoid it, just ask the oil change shop to blow some air.