Reporting my place of employment to labor department?

File a claim with the Board of Labor. If they can't get your money, they will issue you a right to sue letter, allowing you to sue them. You are not entitled to a break. ONLY California has a law regarding breaks - 10 minute breaks. I don't recall how long you have to work to earn it. Anywhere else, don't assume that you are entitled to breaks because you are not. Most places do not give them. If they are given, they are given at the employer's option.

If you are in the US, neither Federal law, nor state law in many states require breaks of any kind.
If your paychecks bounce, you have a valid claim in all states. Google the name of your jurisdiction, and the words 'labor board' to locate the state agency that handles employer/employee law.

There is no federal law on breaks. Those come down to state labor laws. Some states do not require an employer to give breaks

We don't know where you live. The federal government does not require employers to provide meal and rest breaks.
Some states have laws that require breaks. If you aren't in one of them, what the employer is doing is legal.

As for your payments not being good - is a problem.
Request that your employer make good on the checks. If they don't, file a claim with the appropriate wage and hour department (fed or state) or small claims court if your case isn't handled by the dept.

Some states do not have laws about employee breaks. Before you report them, see what laws your state has about that.
How was the bounced check dealt with? If your company was apologetic and immediately made amends, then its not worth reporting.
You might be protected, you might not. Again, it depends on the state laws. You should also look over your employment contract and see what it says about things like this.

Bust their @$$, no mercy.

Report them.