Nowadays most of computers come with wireless adapters but it is an extra option and you need to pay for it. You always can check presence of wireless adapter by going to Device Manager->Network adapters.
Yes, it can. But you have to get a wireless adapter which can be either PCI, PCIe or USB.
The Wireless USB network adapter delivers powerful wireless AC technology to the notebook or the desktop computer. To connect a computer to a high speed internet connection the adapter should be plugged in the available USB port.
You need to get a wireless adapter for that, either external such as USB, or internal such as PCI, PCI-E and so on.
A USB wireless adapter will work just fine on a desktop. A PCMCIA (cardbus) wireless adapter may present problems as most desktops do not have PCMCIA slots. There are ways around this problem however, such as pcmcia-to-PCI adapter cards & the like.
Fiber
Yes, it's. You have to purchase either a PCI wireless card (you will have to open the computer case to install it) or USB wireless adapter (which is easier to install, just put it one of usb ports).
You do not have to use wireless for all of them. You can connect your desktops using cables. And use your laptop with built-in wireless adapter.
Yes, you can. You need to get a wireless adapter which you can get now for $20-30 and more with free shipping. Install it and have with wireless networking.
Yes, you generally need a wireless router to connect a desktop computer to wireless internet. The router provides the Wi-Fi signal that your desktop can connect to. If the desktop does not have a built-in Wi-Fi adapter, you can use a USB or PCIe wireless adapter. According to SafeAeon, using a secure router with strong encryption (WPA2/WPA3) is essential to keep your connection safe from unauthorized access.
The cheapest Compaq Presario desktop PC available is Compaq Presario CQ5110F desktop PC. You can find it on sale when you go to the website of Amazon.
For such purposes you need at least two subnetworks. One adapter cannot be in the same time in both of them. Thus you cannot do that. If you connect your PC through wireless to another PC, and that PC is connect to the router with a LAN cable that it's doable.
One can buy a Compaq Presario SR2020X Media Centre Desktop Computer from various shopping sites such as eBay or Amazon or an online computer site such as Tiger Direct.