Ok I'll address the points that I can:
Yes it is possible to upgrade, or change the firmware on your router to another type. In doing so you will gain access to a far greater set of settings that you wouldn't already have on the factory firmware. Have a look at this article for a good idea of how to do it using DD-WRT:
http://www.howtogeek.com/56612/turn-your-home-router-into-a-super-powered-router-with-dd-wrt/
WPA2 is a great encryption method which basically lets anyone who knows your passphrase connect. What you are also talking about is MAC address filtering which basically adds another layer of security to the connection meaning that if you add MAC filtering to the connection then although you know the passphrase if your MAC address is not in the table you won't be able to connect. A MAC address is just basically unique identifier associated to a specific piece of hardware. You would need to know the devices MAC address before they could connect as you would have to add it to the table in the router's security settings section.
Turning off your SSID is easily possible. That way your network would not show up when a computer or device scans for available networks. People trying to connect would have to do so manually having to enter your SSID name in the connect to dialogue box. Is it worth it? Well it is just another layer of security so yes if that is what you want. Bear in mind though that any serious hacker worth their salt could bypass this without much effort.
Bandwidth calculators. If you want this then that pretty much makes the decision about point 1 for you. You will need to change the firmware on the router if you want this functionality.
I would have a read of that article above and then decide if you are comfortable doing what it suggests. Good Luck.
With all the tests you have done, one has to conclude that your computer's wireless adapter
just cannot manage to work with your router. I hope you have tested with the computer in
the same room as the router.
If the wireless adapter has any way to set parameters, maybe using a manufacturer
utility that came with the computer, then do so.
Or such a utility may be available for download on the manufacturer's website.
Otherwise, try changing some parameters on the router, such as channel or security settings.
You could also try using some other router and see if this works.
Try also to turn off the Windows firewall, just in case.
If all fails and if the computer is still under warranty, ask the vendor for the
wireless adapter to be replaced.
Best Answer
Depending on the OS's you run on your PC's, I assume XP, Vista, or W7, they all have a built in firewall, check each PC firewall setting and turn Off file and print sharing on each PC, set strong passwords on each user account on each PC. If you need to share files on your home network you will need to turn on password protected sharing.
Strong passwords consist of at least 8 characters that consist of Upper and Lower case letters, a number and a special character like ~!@#$%^&*()_+{}
One other thing you can do is to set up a secondary wireless router for you neighbors, put them on their own subnet that is different from yours, this would be the most secure way to isolate the 2 networks.