How did you check your power steering fluid?...was the car running?..it should be.
Read the label on the reservoir carefully and use the appropriate fluid...If the fluid is black and you cannot see through it (wipe some on a rag from the dipstick) then it needs to be changed.
The leaky reservoir cap is common...clean it up as best you can for now...new reservoirs (with internal non serviceable filter inside) are not expensive. Check out Bavarian auto dot com.....they have a great DIY on the site.
There is an o-ring under the cap that flattens out over time and begins to leak..also, those clamps that BMW uses are not adjustable and leak...I replaced mine with adjustable clamps when I replaced my reservoir. (whole thing took about an hour to change the reservoir, clamps and fluid.....but I had to add spacers to the bushings that hold the reservoir in place as they had gotten loose over time)
I believe my car, an 07 took Pentosin fluid...but again, check your reservoir cap for the right stuff.
as long as fluid is moving in the reservoir when the car is running, the powersteering pump is probably okay....fill it up, let the air purge out by running it normally and see if that does not improve things quite a bit....