I was so anxious that I stayed up late yesterday and happiunfortunately got two dark circles. I was so anxious that I stayed up late yesterday and unfortunately got two dark circles.

'Happily' can be correct if you want to say that you were happy you got two dark circles. Because you said 'life has treated me badly' and that you were anxious, I assume you were not happy about this.

I enjoy hanging outspending time by myself. I enjoy spending time by myself.

this is more natural, you don't really hang out with yourself.

When the sun descends, I prefer sitting on the armchair near the lake and feeling the gentle breeze. When the sun descends, I prefer sitting on the armchair near the lake and feeling the gentle breeze.

or alternatively, "...the lake to feel the gentle breeze", if you use and you need to conjugate to feel with I as the subject.

When the sun descendsets, I prefer sitting on thean armchair near the lake and feeling the gentle breeze. When the sun sets, I prefer sitting on an armchair near the lake and feeling the gentle breeze.

-'the sun sets' is a common expression. You can also say 'the sun goes down.' -because 'to feel' is after 'I prefer,' it should be 'feeling,' just like 'sitting.' -'the' is correct if you have already told us about the armchair. The first time you introduce a noun it often makes sense to use 'a'

It seems thatlike the world is stationary atin that moment. It seems like the world is stationary in that moment.

-'seems' is often followed by 'like' when a noun comes next. -'in that moment' I think is more common than 'at that moment.'

I had a half-day off this afternoon and watched two movies during that time. I had a half-day off this afternoon and watched two movies.

It's not wrong to say 'during that time' but it sounds a little awkward.

Two romantic movies with bad endings. Two romantic movies with bad endings.

two movies so endings should be plural, if you were going to use singular it should be "a bad ending" anyway

I’m not sure which I prefer which, BE or HE. I’m not sure which I prefer, BE or HE.

I guess BE and HE mean bad/happy ending but these are not at all common acronyms, I would not recommend using them.

It’s said that heard a musical festival will be held in our city next month, and that day is my birthday. I heard a musical festival will be held in our city next month, and that day is my birthday.

It's said is actually a bit idiomatic and often used for rumors or myths, it doesn't really work here, "apparently" or "I heard" work better here.

It’s sai've heard that a musical festival will be held in our city next month, and that on the same day ias my birthday. I've heard that a musical festival will be held in our city next month on the same day as my birthday.

-'It's said' is not wrong, but 'I've heard' sounds more natural -Because you only said 'next month' it makes more sense to say to then tell us what day, in this case the same day as your birthday.

Can’t wait to see my favorite band cominge here. Can’t wait to see my favorite band come here.

You can also just say 'can't wait to see my favorite band'