If you want to use internet wirelessly, yes you need a wireless router and a wireless adapter for your PC (usually laptops have it).
Yes.
You need to have a wireless router compatible with your wireless adapter and LAN cable of CAT-5 at least. Use the cable to connect the modem and the router, use WAN port of the router. After that configure the router for your needs. And you are ready to go.
There are at least two ways. First, you connect the wireless router directly to the cable modem, and then the switch in the wireless router. You have to connect the cable coming from the modem in the wireless router internet port. Second, you connect the wireless router to the switch, again the cable coming from the switch you have to connect on the wireless router internet port. It's better to put the wireless router just after the modem, but it's not required.
Usually wireless adapters can be connected to computers not to modems.
No. Your computer would connect directly to the cable modem via an ethernet cable.
You can connect your laptop to the Internet with a cable modem, sure. You will need an Ethernet cable to do that. If you want wireless internet, you will need a cable modem, and a wireless router as well.
connect the cable modem to PC using the usb port, leaving you the ethernet porton on the cable modem to connect to the wireless router.
If you want to use wireless connection yes you need a wireless adapter.
yes with an adapter
Yes you can, you have to do that like following. Connect one DSL wireless modemrouter to the cable modem, and another wireless modem connect in the first wireless modemrouter. You have to understand that internet speed on the first DSL router will be rather higher then for the second one.
Yes, you can. You can use wired connection for internet. Meaning, that you can connect your computer directly to the modem through cable, or to the router.
yes you can