lI'm currently using it without the battery installed will there be any long-term effects from this? (will the power source fry the logic board and cpu while it is turned off?)
Really, the only harm that you can make to your battery when you're always plugged in, it's the inactivity of the battery. Just let it plugged all the time and don't think about it. If you use it around one or two times a weak unplugged, it's fine.
Power source won't fry the power source, don't panic about it. People let their desktop computer plugged all the time, and no logic board fried. With would it happen to a laptop? If you're that scared, you can just unplug it for the night if it isn't open.
You should'nt use your macbook without the battery, as the power brick that come with your computer isn't designed to give enough electricity to power when you're doing intensive task (encoding, High quality movies, photoshop, etc.) So it's actually using some of the battery to assist. If you're using your Macbook without your battery, it's automatically down-clocked to 1GHz, so the system will run A LOT slower. And many other component might not work that great either. Gaming would be impossible, for one.