Heater core? Blower motor? HELP!!

I REALLY am in need of some advice and help here!
I own a 2008 Jeep Patriot, one previous owner and it's just hit 100k. I've owned it since 2019 and have had little to no problems with it outside of an alternator that I replaced myself about a year ago. About a month ago I started noticing my front drivers side floor board getting wet, and felt a few drops of wetness in my foot when I'd make a right hand turn. Then I noticed a weird almost slushing sound coming from around the glove box when I'd also make a right hand turn. A week later I realized I had a puddle of water behind the drivers seat on the floor. Fast forward to this week, I go to turn my air condition on because it was hot today and nothing happened. Nothing blows. When I made that right hand turn now; it'll start blowing for a few second and stop again. The noise of the slushing has also stopped. I figured it was a heater core and called around a few places to price one, but the weird thing is I still have heat and air conditioning. I'm no pro mechanic, but in my previous vehicles when the floor board was wet it was always a heater core problem. Rather it was just leaking, it went out or whatever. But I never had heat once I found water on the floor. Not to mention it was always the passenger side floorboards that would get wet, not the drivers side. Today, both floorboards are wet, more saturated on the drivers side rear. There's still a puddle even. & I've sucked it up quite a few times now but it just comes right back. Oh, also; I wanted to add that if I'm driving further than a few blocks to the gas station or whatever; there's a steam coming from my dashboard vents. Has anybody had the same issues or have any insight as to what I need to replace here? My best guess was the heater core as I said earlier in this post, but now that nothing even comes out of my vents rather it's heat or AC, I'm pretty confused!!!
Any help or advice whatsoever is SO very appreciated!!! Thank you for your time!!!

 

does this vehicle have a sunroof?

 

No sunroof!