Landlord Communication/Legal Issues

I need help parsing through what is worth escalating and what isn't. It's been a frustrating month. We just moved into a new apartment (me, my girlfriend, our 6 year old). It's a 3BR apartment in NYC. There have been tons of issues from the start and the landlord is taking her time with some issues she doesn't deem important and flat out not taking care of some others. I need help on how to proceed because I've never dealt with a landlord like this before.

• Upon signing the lease, we asked for a face to face meeting with the landlord. We were told she is too busy and is in nursing school but we can text/call her to communicate with her or set up a future meeting. We did and it took a whole month just to organize a FaceTime with her.
• We moved in July 1st. We had no gas or hot water for the first four days. When I told the landlord, she said she wasn't sure why. I called National Grid and found out that the home had a safety issue regarding the way the hot water heater was venting. It was turned off in October 2025 when the new homeowner (my landlord) purchased the home and she did not know about it. We spent the first week taking cold showers and not being able to use the stovetop to cook. The National Grid technician said she needs to take care of this immediately because the venting issue could cause a fire or carbon monoxide poisoning. It was fixed a day after that and I had to schedule an inspection for a future date to make sure they did the correct fixes.
• After receiving gas, we saw the stove top was broken and needed replacement. She wanted a specific contractor she knew to do the work, so it took another week to get that done. We asked for restitution for the first month's rent for the lack of hot water and having to spend so much money on takeout without a proper stove. She originally said no, until we sent her receipts and expenses. She gave us back $200 of our $3200 rent.
• The real estate agent told us the yard was shared with the upstairs tenant (the owner) but she never planned on using it and it was ours to use. The owner had a shed back there that is hers but that is all. They were building the shed the week we moved in and it was finished during the second week. During that second week, we put a suncast (plastic) closet for camping equipment and other things, and planned to put a small table and chairs back there. The landlord informed us that it was a shared space and we were not allowed to put up "construction" on her property and any table/chairs we put out would need to be brought inside after every use. There is also debris (a propane tank, an oven, garbage cans, wood) in the shared yard and she has "no timeline" on when it'll be cleaned up. With a 6 year old, that basically means the yard is unusable until she figures that out. Fast forward to this week: she is not living upstairs, a new tenant is. So we share the space with THEM according to the lease, not her. The miscommunication between the real estate agent and the landlord is the cause of whatever issues we had in this space.
• The front windows are crank windows. One of them does not close/lock from the inside so you need to go outside on the front porch and close it each time it's open just to lock it.
• We have no DSNY recycle bin outside so our cardboard, cans, bottles, etc. has to be placed in bags on the floor of the driveway. The upstairs tenants have had their garbage ripped into twice by raccoons. When I told her this, she said "Home Depot is out of them, I've been trying to get one." Home Depot is definitely out of them right now, but she has owned the home for almost a year, so you'd think at some point she could have gotten one.
• The faucet was too large for the kitchen sink and two of the cabinets could not open as a result. She had a contractor come replace that a few days after we moved in so we could use the cabinets.
• The dishwasher is broken. We let her know on the second day of living there. She has not replaced/fixed it yet and "has no timeline."
• The refrigerator had a broken draw and broken seal on the door. She replaced the drawer but we have not received a new seal yet.
• The back door to the yard is in our master bedroom. It has a keyhole on the outside but we never received a key. When I told her this, she said "I don't know where that key is and I never received one." We asked her to have a locksmith make us a new key or change the lock since it's an entryway directly to our space. She denied the request and said she will be keeping the door situation "as is."
• There is writing (from a contractor, I assume) on the entryway to the master bathroom that won't come off with cleaning supplies. There is paint drip that has solidified on almost every appliance in the home and in the bathrooms.

She is in nursing school and "always busy" so when we communicate with her, she takes a day sometimes to respond back and when she does, doesn't seem to really answer any questions or alleviate any concerns. The apartment was labeled as "move in ready" and it turned out to be anything but that. It seems like she never actually walked through the apartment even though she claims she did.

It's been difficult with all of these things and the constant need for contractors to come in and out of the space while we also try to make it our own. In my opinion, things like the dishwasher, the stove, and no gas/hot water were just downright unacceptable. The key for the backdoor and the broken window seem like legal/safety issues.

I don't know how to proceed or what to do because we spoke to her about all the concerns on FaceTime and she doesn't seem to either care or know what to do herself. She is young and this is probably her first time being a landlord. Any opinions and thoughts are welcome.