If I tried to sue someone that has an auto mechanic business but file a bankruptcy, now she will open again his business, is this legal?

Whether you can sue someone for a claim against a previous business depends on how the businesses are organized. If the old mechanic business was a sole proprietorship, you can't sue because your claim was discharged in the bankruptcy. If the old mechanic business was a corporation or an LLC and she declared bankruptcy personally, you generally can sue the new business.

The devil in answering your question will be in details that you have not disclosed. If someone files bankruptcy to discharge their debts, generally, they may open a new business to continue working in their trade or career. Using the same or a similar business name may be perfectly fine.

Be very careful about violating the automatic stay or the discharge order. Do not do anything without consulting an attorney very familiar with bankruptcy law.

Yes, this is completely legal. Filing bankruptcy does not end your life.

I have two dozen questions I need to ask you before I can advise you. There's not enough information here to hazard a guess. I do charge hourly for these consultations, but it would save you time and heartache.

Although your question is not entirely clear, I understand you to be asking if it is lawful for a person to close down a business, discharge his or her debts, and then reopen the business. The answer is that it depends on the circumstances. This kind of scam is sometimes known as 'flush and switch.' The important questions include whether the debtor reopened exactly (or nearly exactly) the same business after the bankruptcy; and whether the debtor transferred away anything valuable belonging to the business for less than fair value during the period leading up to the BR. (There are some other questions as well.) You can have this looked into by organizing all the information you have about this person and these transactions, and sending them with a letter to the debtor's case trustee and also the United States Trustee for your federal district. It is not hard to get the names and addresses you will need.