Reply #6: I must say, I'm really not certain, even looking at the picture

[Stinky The Clown]

That *could* be a flue, but it could also just be a duct running off the end of a plenum.

I'd call a furnace guy.

As to the puddling ..... the cheapest fix is, as you note, simply regrading. That may mean adding some dirt to the low spots next to the house. You really con do it yourself. It is just simple grunt labor. You want to slope it so any standing water runs at least ten feet away from the house.

I'd bet the water puddling and the furnace dripping are unrelated. But since I can't see it ..... my real advice is to get a furnace guy now and then maybe talk to someone about getting a load a good dirt in there.