also will random people be able to use my wifi?
I am sorry to say that you obviously do not understand either IP addressing or WiFi.
You have a single public IP address, which is assigned by your ISP. Your wireless router does a number of things. First it assigns different private IP addresses to every device that is attached to it, and second it provides you with a WiFi network.
Without the router, you will only be able to connect one device to the Internet at once. Also, you will have no WiFi at all, as WiFi comes from your router not from your ISP.
You can use only the one public IP address that is assigned to you by your ISP. The private addresses assigned by your router allow the router to support multiple devices simultaneously.
Your WiFi pass phrase is whatever is set up in the router. You should be able to set the pass phrase to anything you want. If your router is set to use the recommended WPA2 (PSK) encryption and you pick a pass phrase of 8 to 63 characters that cannot be guessed easily, then nobody should be able to access your WiFi network unless you tell them the pass phrase.
Since your public address is unique and is the only way the Internet can communicate with you, you cannot use any other public address than the one you have been assigned. The addresses of your devices, connected to your router must be in a different subnet from the public address otherwise the router cannot route information between your devices and the Internet. If you try using addresses in a different subnet, then you might lose partial or total connection to the Internet.
I hope this helps.
You can not change your IP address in any way. The public IP is issued by your ISP and your private IP is issued by the router.
You have two ip addresses, one public and one private.