What is the basic difference between a 'structure' and a 'class'?

The members of a 'structure' are public, by default. The members of a 'class' are private, by default.

It is correct to say, 'The United States', but incorrect to say, 'The Australia'. Why?

'The' is usually used before collective and common nouns. It is never used as a prefix for proper nouns. United States; United is the adjective and States is the common noun. Therefore, it is correct. Australia is a proper noun and does not need 'the' as a prefix.

What is the mistake in the given sentence? "I feel badly for you."

The mistake is in the usage of the word 'bad'. In the given sentence, 'badly' is a linking verb. Linking verbs, such as 'feel', 'seem', 'sound', 'turn', need an adjective and not an adverb. 'I feel badly for you' means that you cannot feel anything for the person you are talking to. 'I feel bad for you' will mean that you feel bad for whatever has happened to the person.