Coolant Expansion Tank Hose

[wolfe]

Well, I fixed the last problem with my car, the windows wouldn't work.
But I never figured out untill today why my car was leaking my coolant. Turns out there is a hose that comes out of the coolant tank. (number 10 on this link http://www.realoem.com/bmw/showparts...01&hg=17&fg=05)
After I turn off my car when it's been running for a bit, That hose just starts spewing nasty brown coolant all over my nice driveway
So, My dad gave a tug on it and happened to pull it out from wherever it leaded too, Probobaly inside the dash.

Questions:

Why does hose #10 on http://www.realoem.com/bmw/showparts...01&hg=17&fg=05 leak after i turn off my car?

Where does hose #10 lead to from the expansion tank?

I noticed I'm missing a hose that leads to my heater core, its the one on the very left of where those three hoses are located on the rubber grommet (# 16 on http://www.realoem.com/bmw/showparts...64&fg=15&hl=28) what in the world is supposed to be going through here?
if fluid , then my car was sold to me with the temporary fix to the heater core, I can see two of my hoses are connected via a metal pipe that probably wasn't supposed to be there, I guess the previous owner connected the two heater core hoses to bypass the heater core because it was having problems.

Well basically I'm trying to say that my heater core has been bypassed previously, when I got my new transmission in my car, the hose fell off probably from them handling the car too ruff and I FINALLY noticed there is no coolant pumping through any of the three heater core hoses and that they have been cut and put together to bypass the heater core. Saving me lots of money thinking I need my heater core replaced because of the cooling.

It all makes sense why My car is leaking now, not my heater core.... but a hose coming from the expansion coolant tank (#10 on http://www.realoem.com/bmw/showparts...01&hg=17&fg=05)

[kalevera]

After I turn off my car when it's been running for a bit, That hose just starts spewing nasty brown coolant all over my nice driveway

Coolant's not supposed to be brown. Brown coolant suggests problems.

So, My dad gave a tug on it and happened to pull it out from wherever it leaded too, Probobaly inside the dash.

Actually, it's the pressure overflow bleed from the expansion tank, it drops down to the frame rail.

Questions:

Why does hose #10 on http://www.realoem.com/bmw/showparts...01&hg=17&fg=05 leak after i turn off my car?

Either too much pressure in the cooling circuit, or the expansion tank cap is bad.