I'm a salary paid employee, if my company decides to shut down for a day, is it legal for them to dock my pay?

You are correct in your assumption that "salaried" (exempt) means you are paid for a full week at a time, regardless of the number of hours worked. However, the company is permitted to shut down for a full day and not pay its exempt emloyees for that day. It sounds from your description that they are taking advantage of this by shutting down frequently and not paying employees. You might want to contact the department of labor in your area about their shady dealings: www.dol.gov

Check your employment contract agreement or employee handbook. You may have agreed to those conditions and forgot. If you never agreed to those conditions, then you have a case. You can file a wage claim or you may file a case in small claims court.

Call the labor board in your area and ask them that question and they will tell you. If you are a salaried employee it would not affect your pay; but, if you are an hourly-paid employee, I believe they can. I would call the labor board before I would suggest ill feelings about your pay to your boss!

What state do you live in? In texas, you should have a contract you signed when you started the job stating the salary you should be paid, and if they can change the amount. Re-read that document to ensure your wage cant be changed. If it cant, send letter. If they don't pay you, take them to small claims.

Depends. Are you non-exempt or exempt? If salaried exempt, I do not believe they should dock you. But, you need to ask a lawyer.