Spread (1)

Perhaps this in not the best word. ( A person 'spreads' things like 'gossip' or 'rumours'.) The best collocations for 'criticisms' in this context are 'expressed' or 'put forward'.

our school system's hindrance. {2}

Poor word choice

named for {3}

or 'named by' in British English

information era {4},

Punctuation

we'd better have our children well prepared to face the future job market, otherwise the globalized competitors will knock them down.{5}

Good

politics' {6}

Word form

not only the schools are {7}

Word order

a recycling compulsory course{8}

I suggest saying: a compulsory retraining course'

Should (9)

Poor word choice

Out (10)

Wrong or misused preposition

Should (po 10)

Poor word choice

Hole (po should po 10)

Spelling -whole

indemnify all of them{11}.

I'm not clear about what you are trying to say here!

available for a conversation.{12}

How would the professor be able to contact you? Perhaps say: 'I am happy to be contacted by email at....'

faithfully{13}

Normally the convention is to write 'yours sincerely' if you know the name of the person to whom you are writing, but you wouldn't lose marks in the exam for writing 'faithfully'!