English grammar

1.
"an" accident is CORRECT. The other ( ) are CORRECT.
This is the first time this "accident" is introduced, so it is "an" accident; if later in the writing to describe the details of this "accident", then the writing should be "the" accident. e.g. the cause (main reason) of the accident is ...

2.
but it broke down several times -> but it had broken down several times...

"What you will want is a second-hand mini," -> "What you want is a second-hand mini,"
Although the "action" seems to be future tense, like the following sentence "will get (buy) on tomorrow", but this should say "what you want" means you opion of the fact of the item of "want". Sometime in giving opion, you may also say "What you should do is...", but "do" is a suggested action, "want" is in the mind, so you do not say what you should want but just always assume the fact of the"want".

1.
Since it is your first time to mention the term 'accident' and 'accident' is not a professional noun, you must use 'an' instead of 'the'.

2.
Last June my brother wanted to buy a car. He had an old scooter before but it 1)had been breaking down 2)for several times during 3)spring. "What you 4)want is a second-hand mini," I suggested. "If you give me 5)money," he said 6), "I will get one tomorrow."