Ok so I'm not sure all those are related. Few things:

1. When it grows a new leaf - it almost starts to wilt. Leaves get super weak and some break. Once new leaf is out - all is good.

2.Lately I moved to another room, I'm pretty sure it has same amount of light but it's warmer here. It started to drop water. It did this before but occasionally, now it does it every day. The soil is dry to the touch but I'm afraid to water it... I water it every 3-4th day because it dries out fast.

3.And now it's getting dark spots on its leaves. Some larger and some along the whole leaf but tiny.

Please help! This plant is my first plant baby and I got it so tiny and it's so big now. I'd be devastated to lose it.

Hi,
I think it's looking very good! I would not be worried about the minor flaws.
I'm glad to see a relatively small container for the plant. Watering too much seems unlikely.
Is there a hole/can you allow water to drip if there is too much?
Probably likes as much light as you can possibly give.
Disclaimer:
I've only grown a banana, once or twice, outside, whole different thing.

Dripping water is called guttation, it's caused by the roots unable to soak up all the water, as Sally asked are there drainage holes in the pot? I use a chop stick to check out the moisture level in the soil, when you water, do water enough that it drains out the holes, if there are some?