I would like to know if I plug my router to the back of my Mac via Ethernet, will I get a a faster data through than relying on my existing wireless(.g) set-up?
As I am having the computer and the wireless router in the same room, I start to worry about what the radiation effect may have to my well being. Also, when two equipments are being put so close together, I might as well link them up by wire.
Well, the connection through a physical connection will likely be 10, 100 or perhaps 1000 Mbps (depending on the ethernet card/connection your Mac has), compared to the 54Mbps of wireless g. However, your connection to the internet is going to be nowhere near either of these two limits (i.e. < 2 Mbps), so you're unlikely to notice any difference if all you're doing is accessing the internet.
If, however, you have a home network and often transfer files between machines, you may well notice a difference if you shift machines to physical from wireless (though, of course, both/all machines will need to be on physical for you to notice the effect).
I, for instance, link my desktop machine to the wireless router using a LAN cable, because they're right next to each other, but use the wireless capabilities of the router so I can surf using my laptop from other rooms. If I need to transfer files from laptop to desktop, I temporarily wire in the laptop to another port on the router, boosting transfer speeds from 54 Mbps (at best) to 100 Mbps (guaranteed).