The Bureau of Citizenship and Immigration Sevices (BCIS) deals with legal entry and legalization of aliens and the naturalization of legal residents. This is the agency that grants extension of non-immigrant visas.
INS has made it much easier for you to receive and replace your EA card. Please visit the INS office and you should be able to get your replacement card in a couple of days. You can continue to get the card replaced until you get your I485 processed.
Sample of an INS employment aurhorization card
You should first contact the closest foreign consulate office for detailed instructions. Extension of your visa will depend on whether or not you have a valid passport and what the date stamped on your I94 states.
Sample of an I-94 card
The Department of State web page details what kind of visa they may apply for and also has a list of all the U.S. Embassies, Consulates. Generally, your friend/relative will need to come prepared to prove that they are not planning on immigrating here they should provide evidence of property, financial statements, ties to the community through work, organizations they belong to, family and friend ties. You may have to act as the sponsor for your friend/relative which means you can prove that you will be financially responsible for your guest. Depending on the visa, you may need to apply to the INS for approval.