Yes, why not? Just make sure you do it right otherwise the clerk will bounce them back at you. Many State and local bar Associations make lawyers available to review non contested divorce papers. See if your local or state bar has such a program.
Yes, you can file a divorce on your own. Make sure it's done right. At the end of the case, you should receive a Notice of Entry of Judgment to let you know that it's been finalized. Make sure you do it right!
Sure you can. In many jurisdictions the clerk of court has forms you can use to file your case properly. If the divorce is uncontested, if there are no children, if the marriage is relatively short term, and if you and your spouse have not accumulated any significant money or property, this should be no problem. If however it is a long term marriage, and there are disputes regarding children, division of property and the like you are better off hiring a lawyer.