She has a lot of works to do today. (Improve)

• A. lots of works
• B. a lot of work (Answer)
• C. many works
• D. No improvement

'Work' is uncountable when meaning tasks/occupation. It has no plural form 'works' in this context.

He discussed about the problem with his friends. (Improve)

• A. discussed over
• B. discussed (Answer)
• C. discussed regarding
• D. No improvement

'Discuss' is a transitive verb — it does not need 'about'. Simply 'discussed the problem'.

He spoke to the audience for two hours. (Improve)

• A. spoke before
• B. spoke in front with
• C. No improvement (Answer)
• D. spoke among

'Spoke to the audience' is correct. No improvement needed.

They reached to the station on time. (Improve)

• A. reached at
• B. reached (Answer)
• C. had reached at
• D. No improvement

'Reach' is a transitive verb — it does not need a preposition. Simply 'reached the station'.

She is a vegetarian and does not eat no meat. (Improve)

• A. does not eat any meat (Answer)
• B. does not eat some meat
• C. eats no meat
• D. No improvement

Double negatives ('not...no') are incorrect in Standard English. Use 'does not eat any meat'.

She is much more better than he was. (Improve)

• A. much more good
• B. much better (Answer)
• C. very more better
• D. No improvement

'Better' is already comparative. 'Much better' is correct. 'More better' is a double comparative.

He said to me that he will come tomorrow. (Improve)

• A. he would come the next day (Answer)
• B. he shall come tomorrow
• C. he will come next day
• D. No improvement

In reported speech, 'will' changes to 'would', 'tomorrow' changes to 'the next day'.

Let us wait here until he will come. (Improve)

• A. until he comes (Answer)
• B. until he came
• C. until he shall come
• D. No improvement

In clauses of time introduced by 'until/till/when/before/after', use simple present for future meaning.

He could not cope up with the pressure. (Improve)

• A. cope up at
• B. cope with (Answer)
• C. cope under
• D. No improvement

'Cope with' is the correct phrase. 'Cope up with' is incorrect.

He entered into the room quietly. (Improve)

• A. entered in the room
• B. entered the room (Answer)
• C. entered unto the room
• D. No improvement

'Enter' is a transitive verb that does not need 'into'. Simply 'entered the room'.