Theoretically, A isn't faster than G. It's the same max throughput of 54Mbps. That said, it does use the less crowded 5.4Ghz frequency so it's range is better and you do tend to get faster speeds due to the better/stronger signal.
You shouldn't see any speed difference with G devices if the router is set to mixed or not. You would see a decrease in speed if you are using B devices at the same time though.
Wireless, in general, is very distance and location dependent. For G networks, if you are getting 10 to 12 Mbps you are doing pretty well even under optimum conditions. If you are getting a lot less than that you can try these things:
First: Test the speed of your wireless network by having your PC and router in the same room. If you don't see an increase in speed, you simply aren't going to see any better on that hardware.
If you do see an increase in speed by having them closer together try these:
-Change the "channel" that your router is using. There could be interference on the default.
-Reduce the distance between the router and your PC
-Move the router so that there are as few physical obstructions between your PC and it.
-Make sure that your transmit strength on the router is set to maximum, if there isn't an option on the router to do that, you might be able to use 3rd party firmware to boost it if your router supports it.
-Try using hi-gain antenna on the router.
None of this will guarantee a faster connection, but often do help.
If they don't work you can try using a wireless extender/access point or Try using just the A network if all your hardware supports it.
If you are already getting 10Mbps or better then you simply aren't going to do much better on a G network. At that point your only option is to move up to N.