hello all! I am new to the world of plant, it’s something i have always wanted to do but after killing a cacuts a few years back i just assumed it wasnt for me and gave up— until now.

about 3 days ago i purchased a small Pothos plant as well as a parlor palm, thinking they would be a good place to start. I placed my palm on A north facing window sill. It looked beautiful, and seemed to be in great shape. the soil was wet when i purchased it so i have not watered it since (although it did rain fairly heavily and came in thru the window for a bit of time before i realized and closed the window!) that was 2 days ago. yesterday i noticed some brown tips, as well as a bit of browning on some stems/stalks (??) see pic- i apologize for my lack of knowledge on the vernacular!

I moved the plant away from the window as i live in NYC and it has been pretty cold. Also, the heat in my prewar building is EXTREMELY DRY and i have absolutely no control over it. Considering putting the palm in my bedroom where we keep a humidifier. Wondering if there’s anything else i can do to help this plant. its still in fine shape overall but i am worried because it was in perfect shape just 3 days ago and i fear I’m on my way to killing another plant :-(

my main concerns:

unsure if soil is draining well, it still feels moist.. is this normal? How moist is too moist? (in terms a beginner would understand please!)

and secondly, the roots seem to be growing thru the drainage holes!! Unless these are not roots?? (See pics) everything i read says palms enjoy being a bit crowded but this seems excessive, no?

any advice would be appreciated! thanks