Hi Veronica,
In most cases, the rack and pinion will leak at the rubber boot on each end or on one end. The bushing and seal in them start leaking and it goes into that boot (see pic 1). The boot, once so much gets in it, starts to leak. Check to see if that is where it is leaking.
A plug would prevent power assist and is unlikely. I would think it is more than likely related to the pump. If there was a clog, I would expect the pump to make a noise (much like when trying to oversteer) indicating excessive pressure.
Other than the noise, do you have power assist? Also, here is a link that explains how to flush the power steering system. You may want to start simple with something like this.
https://www.2carpros.com/articles/power-steering-fluid-flush
Also, you indicated two leaks. Here is what I suggest. Look under the vehicle for where it's wet. Use a cleaner to wipe it down and dry it. Then drive the car and inspect it again after the drive. See if there is evidence of where it is coming from.
One other thought (sorry if I'm driving you nuts). You are having a shifting issue. You indicated one of the leaks is below the trans/rack, is the transmission fluid full? If it's getting low, that could be half the problem. The pan gaskets are known to leak. Let me know about that.
Let me know what I can do to help.
Take care of yourself, and Happy New Year.
Joe
See pic below.
Image (Click to make bigger)
Saturday, January 1st, 2022 AT 9:25 PM