Hi, and welcome to the forum!!
If your problem is in the liner, then you need to look around the level of the pool water, because the leak will stop when it gets to the level of the hole/tear. I'll let some of the construction gurus around here address the skimmer possibility, but just wanted to welcome you and let you know we'll try to get you swimming as fast as we can!
I think trying to shock the pool at this point, without a working pump and filter, will be a waste of time and money, especially if there is a liner repair/replacement in your future. You have to make frequent additions of bleach and get it circulated in order to kill the algae, and then the filter is required to get the stuff out, so I think I would wait until you get the pump/filter working to address the water. No need to drain and refill if you don't have to, you'd be amazed at what kind of messes a little (OK, a lot) of bleach can fix!
Janet
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