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Check oil level. May just be a little low.
Is it very loud when you are running, like an exhaust breakage before the muffler loud?
Use that warranty, and take to the dealer. Be as descriptive as possible to the mechanic.
Definetly sounds like an alternator issue. Did you 'jumpstart' the vehicle before you replaced the battery?
I will assume you mean recharge the AC system. From the air compressor you will see two metal lines coming out. A thinner one and a wider one. The wider one is the low-side (lower pressure side) Follow the wider one till you find the schrader valve.
What is the question?
Then there is a leak in the system. The leak must be repaired and sealed or the AC will never hold a charge. Take to a shop and tell them you need the AC system checked with a dye test to locate the leaks.
Take to an autozone and get a free check engine code read and post the result on here to further assist you.
Parasitic drain agree with #1. While parked in garage, turn off all light or do at night, look around the vehicle for a light somewhere on that shouldn't be. One usual suspect is the under the hood light. Otherwise, take to a mechanic.
No, the line is too thin. The wider pipe is the low-side which, is where you use the AC recharge kit.