Agree

I am agree, are you agree? (Incorrect)

I agree; do you agree? (Correct)

"Agree" is a verb, not an adjective.

I agree Mr Chan; do you agree what he said? (Incorrect)

I agree with Mr Chan; do you agree with what he said?

You agree with a person or idea and you agree to do something.

Across

I acrossed the road. (Incorrect)

I crossed the road. (Correct)

The verb is "to cross" while "across" is an adverb or preposition, as in:

I went across the road.

According to

According to my opinion, we should go hiking. (Incorrect)

In my opinion, we should go hiking. (Correct)

"According to" is used with another person or source of information and is not used with 'opinion'. 

According to all these reasons, she decided to change jobs. (Incorrect)

For all these reasons, she decided to change jobs. (Correct)

"According to" is not used with "reason".

Common English Errors in HK (2)

Many of friends came to see her off at the airport. (Wrong)

Many friends came to see her off at the airport.
Many of her friends came to see her off at the airport.

'Many of' is only used when followed by a definite group, some of whom are not included in the 'many'. When simply followed by a noun, 'many' does not take 'of'.

Common English Errors in HK (1)

Barry spoke foul languages. (Wrong)

Barry used bad language.

'Language' is only plural when it refers to different languages. 'Foul' is a strong word and can be used for really obscene language, but 'bad language' is more common expression for swearing. And the verb is generally 'use'.