Nearly all computers have a wireless adapter to connect to the internet. If not, an ethernet cable connected to the router will get you online. Type “device manager” in the search box by the Windows icon in the bottom left of the screen. See if you can find a wireless adapter listed under Network adapters. Right click on it, find Properties and then investigate if it's working properly.
No, a TAP adapter is something to do with VPN software that hides your IP address eg ExpressVPN or Cyberghost. If you haven't a wireless adapter they are very cheap to buy on ebay or Amazon. It's a dongle that plugs into a spare usb socket.
No, it'll include the word "Wireless." What is the computer make and model? If it's a laptop there will be a wireless card inside but sometimes with a desktop it is an extra and a usb wireless adapter is the easiest solution. Did the computer previously connect to the internet wirelessly ?
There's no wireless adapter but I recommend that you get one. You can reach your ethernet adapters by going from Control Panel to Network and Internet to Network and Sharing Centre. Next View network status and Tasks. You'll see Change adapter settings. From there see what you can do by right and left clicking with the mouse. If you get a usb wireless adapter it'll show up in there too. I'm wondering whether you are running Windows 10 on a recent PC. If not maybe it's time to think about upgrading to a more recent model. Everything has moved forward rapidly in the last few years. Wireless connection will make life a lot simpler for you. Windows 10 will detect the wireless adapter and connection to the router will be very easy