A:AnswerYes. Think of it this way: the wireless router takes your internet access and distributes it (without wire) to your devices. However, you have to have a way to get access to the internet. So you have to have a modem to receive and forward your internet access. Some firms and some devices combine a modem with a wireless router. This device is the wireless part only.
A:AnswerYes, You can install a second router in the home. You could get a range booster for the current router. You could also get a Better router like a NETGEAR - N750 Dual-Band Wireless-N Gigabit Router with 4-Port Ethernet Switch which would give you better signal for the whole house and mostly increase your thought-put over all. Do to the face the wireless/modems from service providers are no the best for wireless speeds. (Fun fact. Charter offers a wireless router but does not support the wifi only hardwire and does not guarantee any connection speed with it.)
A:AnswerPretty much any router will work after the signal from the ISP is in your home. The modem will provide a ethernet port will go into the "internet" section of any router and a way u go.