Can you buy a faucet and install it by your self

You can buy a faucet lots of places and should be able to install it. Most are held on with nuts that screw onto the tubes the supply lines attach to. Most supply lines have shutoff valves on them or you can shut the entire house off. You can usually change one with just a pair of pliers or pliers and an adjustable end wrench, commonly known as a Crescent Wrench.