One has to be clear about the difference between firewalling and securing your network against people using the signal.
A wireless router broadcasts it's existence to anything up to about 100 metres away, sometimes more, but usually less.
The methods used are moderately smart, so you don't have to do much to connect. If your PC has been on a wireless net before, it's entirely possible it may "adopt" a router without asking you, or by flashing an unhelpful message.
Thus it's not impossible to accidentally attach to your neighbours router if it's "nearer" allowing for walls than your own.
The default "name" for most routers is either it's manufacturer or the model type. Given that there aren't that many manfuacturers, you may actually think "ah Belkin, must be mine".
This used to be absurdly unlikely, but these days so many homes have wireless, it's quite possible to "see" multiple networks from your home, and for them to see you.
Yes, it is possible to "see what you are typing". There's s/w for this sort of thing, and the utter lack of any decent security is one reason I do not use online banking, even though my home PCs have quite good security. As it happens in my last job I was in charge of the network HM Treasury uses to monitor investment banks, so I have some idea of how crap retail banks web stuff is. Short version is that if you turned up with an IT service at a household name bank with the sort of security they give to their customers they would quite literally laugh in your face.
Very few home firewalls maintain any useful record of attacks upon them. Thus you could be under attack right now and not notice except for your link being a bit slower.
A firewall looks at the lumps of data flowing through the machine, and if it doesn't like what it sees, blocks the packets. Thus the F/W on your PC has some chance of stopping bad stuff coming in from the internet, but will trust a neighbour's PC , as its default.
The firewall that comes in nearly any wireless router looks at stuff from the net and linked PCs quite differently.
The default setup as it comes out of the box, is to trust any system on your "side" of the firewall. It will not stop them using the net, and it will not stop them being able to reach your PC. The odds aren't very high that your neighbour has the skills to hack into your PC, but there are much higher chances that he may be infected with something nasty that will try and recruit your PC to some nefarious purpose.
Your Windows F/W may resist such hacking, but it's from Microsoft. They're not exactly the #1 trusted brand for security.
To secure your router at least to a minimum, you need to follow the instructions on the manual, or the manufacturers web site. Decent ones like Linksys allow for the data to be encrypted and only certain network cards to talk to it.
They also can block addresses and only allow web access at certain times, which may be useful if you have kids who need to be "rationed".
The process for this is not all that tricky, but does require that you read the manual, and ensure that you know what you are doing. First thing of course in that process is to find the way that you can re-set the router back to "factory settings" :)
One "factory setting" is that the password for the router is standard, and published on the web.
Typically the router is shipped so that you aren't allowed to login to it as an administrator from the outside net.
But your neighbour can, since the router has no way of knowing that they are next door, unless you tell it.