This can be a tricky question because a router will allow you to share the connection with more computers/peripherals which has the potential to lead to more data usage. However, a router itself WILL NOT use any more data than plugging your modem directly into your computer. You will only be using data when the computers connected TO the router (either via WiFi or ethernet) are using data.
When you insert your wireless modem into a mobile broadband router it will automatically establish a connection to the internet. While your card is in the router, the connection will remain on 24/7, allowing you connectivity from all of your devices. However, even though your device is connected all the time, it doesn't mean that it's transmitting data constantly. When you're not using any of your computers/peripherals the modem will go into a dormant state (connected but not actively transmitting data). When you turn your computer on or use a device that requests information online the modem goes out of the dormant state and begins actively transmitting data again.
While the router itself does not use data, sometimes using a router can result in more data usage than you're used to, because you're allowing more computers/devices to share the connection. Here are some things you can do to make sure you don't waste data:
1.) Set up wireless security - Enabling WEP/WPA security will ensure that nobody else can join your network and use data without your knowledge
2.) Turn automatic updates on your computer off and have the system notify you when they're available, instead - allows you to choose the updates you really need/want to download instead of wasting data downloading every update available
3.) If you're connecting your router to a Internet capable TV, Blu Ray Player, Satellite receiver or game system, check the settings to know when a feature may access the internet, ie - accessing Netflix from a Blu Ray player will use data.
Sources: Will Using A Router Eat Up My 5GB or 10GB Data Allowance?
Yes. A little.
WiFi is orders of magnitude less reliable than a wired connection, and gets worse the farther away you are, and the more interference in your area (very bad in dense housing, campuses). It also worsens with more devices connected.
inevitably, this will result in external network traffic to or from devices needing to be re-transmitted. This does happen in wired networks, but it is orders of magnitude more common in Wi-Fi (again, especially in poor conditions)
In the end, this won’t likely be significant unless your signal is very poor - but you wouldn’t want to use this connection anyways as it would be very slow.
