'The football team is doing well!'
no it is not a correct sentence.
"He is good" is correct. 'He' is singular, 'are' is for plurals.
Always do good is correct and means what it says. "Always be a good doer" means something slightly different from what it says. A good doer is person who is known for doing good, not necessarily a person who does good.
No, Are Jack and Jill good football players is
One good workout for American football is doing pushups.
This sentence is completely correct.
"he is a great chess player" is grammatically correct, but the rest could be better. No one really says footballer, a better choice would be Football player try: "he plays football and chess well." or "he's great at both football and chess."
The person's a criminal for doing what he did.
When a book is good, I get lost. It was this sentence grammatical corrected.
Your brother is exceptionally good at football.
If the person is doing something positive according to their beliefs and morals, they are doing good. If they are doing something properly and correctly, they are doing it well. The distinction is this: doing good means achieving worthwhile ends, especially to society's benefit, while doing well means succeeding, especially at making money. In the first case, "good" is a noun, the direct object of the verb do. In the second, "well" is an adverb modifying the verb do.
"My mathematics is good" is correct out of the choices given, but a better sentence would be "I am good at mathematics".