I'm not an expert, so I can't say I'm totally accurate, but here's my take on your questions:
A firewall protects outside users from accessing your machine while allowing you access to the internet. A good firewall can make it look like your machine doesn't even exist on the internet.
Your pop-up problem is probably some piece of software on your machine that is making requests. There is a lot of adware/spyware out there that will do this sort of thing. There's software out there that can clean the adware/spyware from your machine. Maybe someone else on this board knows what works (I haven't used this myself).
The best way to prevent getting spyware/adware on your machine is to be *Very* careful what you install, especially if the source is some website on the internet. Gator is a company that creates adware, and is very difficult to remove from your system once it's been installed. Some shareware programs out there have gator software built in, so if you install some software, you end up installing Gator as well.
Bottom line, a firewall will not protect you from this sort of software. A firewall will only protect you from outside users gaining access to your computer.
The different wireless protocols are a bit confusing, but which you choose will limit your bandwidth. 802.11b's theoretical maximum is 11Mb/s (though with some manufacturers, if you buy their router and their wireless card, you can get up to 22Mb/s). 802.11g's theoretical maximum is 54Mb/s. If the bandwidth you are getting on DSL is, say 8Mb/s, then going with b or g won't make a difference. If you are getting 40Mb/s over DSL, then you will get faster bandwidth with g than with b.
For internet browsing, email, etc. I don't think most people will notice. For large file transfers, there might be a more noticeable difference, but again it depends on the speed of your DSL connection.
The frequency can be a problem with cordless phones and microwaves, but I've heard varying accounts. Some can talk on their cordless phone while at their laptop with a wireless connection - no problem. Phones and the wireless protocols can access different channels to send data, so there isn't always a conflict. I've found microwaves to be a bigger problem, but I've only noticed when my laptop was in the kitchen - and for us, the microwave is only on at most 5 minutes at a time, so no big deal.
And the freedom with wireless is great. If only there was a safe, cheap, and efficient way to do wireless electricity...