What is the ruling on performing tayammum for prayer when water is available half a kilometer away, and is that considered a violation of the Sunnah of the Prophet, peace and blessings be upon him?

As long as seawater is accessible, it is not permissible for you to perform tayammum, and your prayer is invalid. This is based on the Almighty’s saying: "And if you find no water, then perform tayammum with clean earth." A person is not considered to be without water unless they have exhausted all means to obtain it and failed. The procedure for seeking water involves searching in one's belongings and around the area, and inquiring about it from companions or knowledgeable individuals. One is obligated to seek it if it is nearby and there is no fear of harm.