She didn’t want to go back to the shops because it was very late.

• Correction: Replace "lately" with "late". "Lately" is an adverb, while "late" is the correct adjective here.

It is the largest city in Europe with a population of over eight million.

• Correction: Replace "larger" with "largest". The superlative form is needed to describe the biggest city.

If you write the essay carefully, you will get a good mark.

• Correction: Replace "careful" with "carefully" and "good mark" with "a good mark". "Carefully" is the correct adverb, and "a good mark" is more appropriate.

Thank you very much for the present that you sent me.

• This sentence is correct as is.

The child ran fast to get to school.

• Correction: Replace "fastly" with "fast". "Fast" is the correct adverbial form.

The women would spend their time making bread and bullets for the soldiers.

• Correction: Replace "women" with "women" (already correct) and "to make" with "making". "Making" is the correct gerund form.

She finds housework boring and doesn't like to stay at home all day.

• Correction: Replace "bored" with "boring". "Boring" is the correct adjective to describe housework.

We are interested in the conservation of forests.

• Correction: Replace "of" with "in". The correct preposition here is "in".

Sometimes it takes me about three hours to finish my round.

• Correction: Replace "finishing" with "to finish". "To finish" is the correct infinitive form.

Stories are the best way of teaching moral lessons to young people.

• Correction: Replace "goodest" with "best". "Best" is the correct superlative form