Re: What type of UART I need ?
Firstly, a UART alone will not fix it. If the problem is corrupted firmware in the router, a UART might be able to let you upload new firmware so make sure you have it ready to use. In most cases, you also need some software from the router manufacturer to allow you to communicate via the UART interface.
Both the ones you found should be OK. The voltage you need should match the voltage INSIDE the router so it would probably be best to measure it before deciding on 5V or 3.3V. Ignore what the routers external power requirements are because it almost certainly has an internal power supply and regulator that drops it to either 5V or 3.3V (rarely to 1.8V).
Using 3.3V on a 5V device might work but would be outside manufacturers specification, however it probably wouldn't do any damage. Applying 5V to a 3.3V device is quite likely to kill it though.
Brian.