Well I'm not a fan of the band, but from the passage you quoted, I think "tightly arranged compositions" means that the songs in this album are composed or written as a whole. As a reslut, each song recorded is tightly related to the other in its lyrics or melody in the album. In contrast, the former album has more live songs than studio recordings.

News article that I read before about child abuse in a daycare center.

I read an article about abusing young child in a day care center on a Korean website. In the article, a daycare center teacher was arrested for assaulting (Well personally I think the word 'assaulting' is too aggresive in this scenario, and the word 'abusing' or 'mistreating' can be used instead) a young child. In a CCTV footage from the center, the teacher hit (simple past tense) the young child and knocked her down. There were several children in front of the teacher, and they seemed to be afraid of her. Child abuse in a daycare center has become a huge/top issue in Korea. Therefore, setting up a CCTV in a daycare center has become mandatory recently, but even though there is a CCTV, child abuse is still happening.

Mistakes in grammar can be avoided by caution, if you keep that in mind and check every sentence upon finishing. Over time, you will be able to write correct sentences naturally.

My volunteer experience in a senior care center.

I started to help elderly people in a senior care center, because I wanted to have volunteer experience in the health care field in Canada since I was a nurse in my country (Remember to pause appropriately when you have a long sentence). I have volunteered since 3 weeks ago, and I do it on every Tuesday morning. My major role is encouraging and bringing residents to join a recreational program or assisting seniors. They either have dementia or Alzheimer's disease, so most of them hesitate to interact with others. They need a someone (you either use someone or a person) who can encourage their social activity (Actually, this sentence will be better expressed using passive voice).
In the senior care center, I met really nice elderly people and I really enjoyed to spend time with them. Since I have started volunteering (it's a verb. start doing something. if it's a noun, it refers to the person who volunteers) a few weeks ago, some seniors can still remember me and they seem to be happy to spend time with me, so I feel rewarding.

Words added or removed are marked in yellow while advice given is marked in grey.

Well I think your vocabulary and grammar are quite impressive and you made few mistakes. Genernally, the whole passage is coherent and reads smoothly. The only thing worth paying attention to is that you need to pause when expressing, and limit the use of the word 'so'. Sometimes you can replace it with other words or phrases like 'thus' or 'as a result',etc, or split it up into two sentences.

Good luck with your study and have a nice day.