No you cannot claim anything for utilities you pay.
There is not a rent deduction or credit on your Federal return. If your state has anything for renters you will be prompted to enter your rent info when you complete your state return. As far as I know, the states that have anything for rent are Arizona, California, Connecticut, Hawaii, Indiana, Iowa, Maine, Maryland, Massachusetts, Michigan, Minnesota, Missouri, New Jersey, Rhode Island, Vermont, and Wisconsin.
No. If you are referring to normal living expenses for a home, renters cannot deduct rent or utility payments from your federal return. Check to see if you pay property taxes as part of your lease agreement. If you do, you can deduct that portion of your rent or any property tax you pay directly.
Yes. If you are operating a business out of your rented location and it is your home you may be eligible to take the home office deduction for rent and utility expense for the portion (square footage) of the home that is used for your business.
Yes. If you are operating a business out of a rented location and the entire facility is used for business, you may deduct your rent and utility expenses.