Hello Alison and thanks for this essay.

Word choice/Word form/Usage

• painting and music have no straight influence on people's lives ==> direct influence
• Allocating in the art is totally wasting the government's money ==> Allocating money for art is a total waste of government money.
• art is a part of cultural ==> art is part of culture
• It is clearly the government should found in this area ==> It is clear that the government should fund the arts.

Introduction

I like your phrase '...which is a misconception', but I would like a Thesis sentence after it - a sentence that makes your opinion even clearer and explains what you will do in your essay.

I will explain why supporting music and art is a vital government responsibility.

Unnecessary words

Apparently and agreed by many people, art give us immense enjoyment

Art gives many people immense enjoyment

Painting and music, in many instances, indeed bring a great deal of entertainment to us, which diversifies our means for improving the quality of life.

Painting and music entertain us and improve our quality of life

Run-ons and Fragments

The first comma in this sentence is incorrectL

Consider listening to a beautiful song sitting on the sofa after a whole day’s work, it really relieves the tiredness and pressures

It's easy to fix this - just use a full stop! In general with commas, the rule is: "If in doubt, leave it out!"

Consider listening to a beautiful song sitting on the sofa after a whole day’s work. It really relieves the tiredness and pressures

Articles

the tiredness and pressures ==> tiredness and pressure

Simplify

You wrote:

Listening to music alleviate intense sentiment .

I'm not sure what this means. Simplify!

• Listening to music improves your mood. 
• Listening to music calms you after a stressful day.
• Listening to music can be a very emotional experience.

Shorten: Monster Sentence Alert!

Here's a monster sentence - 45 words!

Currently, many children are sent to some professional schools to learn painting, music, dancing and other domains of art by their parents, simply because they know learning art can mould a person’s characteristic and upbringing well, from which their children are benefited throughout the lives.

Why passive? Why so long? Remember - aim for an average sentence length of about 12 - yes, twelve words! Some sentences can be longer - say up to 25 words, but most should be short. Have a mix.

Here's one possible rewrite - Two sentences with a total of 35 words (average sentence length: 17 - Getting there!)

Many parents send their children to classes in painting, music, dancing and other art forms. They know that art helps to mould young minds, and that the skills learned will benefit their children for life.

Shorten:  A small monster: 35 words

It is clearly the government should found in this area, or the public museums and galleries would all be closed and that is obviously a disaster, which is the last thing we want to happen.

Don't have new information (e.g. about galleries closing) in the conclusion - this should have been in the body. Look to the future:

Clearly, governments should fund art and artists. Our museums and galleries should be places where art can flourish and be available to all the people.

Overall, some nice ideas and phrases. But watch out for those monster sentences, and keep things simple!