To attempt to answer your first question, the idea is to create an environment in which algae cannot compete with the plants. While we know that excess nutrients are not the cause of algae, no one really knows exactly why, so you're not alone. All we know is that plenty of healthy, growing plants that are not limited by nutrients or CO2 = very minimal algae. One way of looking at it is that as long as the plants are using the available energy (light) to the fullest extent possible, it makes it difficult for algae to take hold, so the best practice is to make sure that light is the limiting factor instead of CO2 and/or nutrient levels. Algae is opportunistic, and will survive by scavenging the tiniest amount of nutrients, but if there isn't much excess light available (and CO2 and nutrients are both abundant and stable), for some reason algae seems to sit back and let the plants do their thing, waiting for the opportunity of conditions that are better suited to its propagation. If this was not true, aquatic plants would not even survive in nature since they would always just be overtaken by algae.
Yeah, the "balance" idea threw me off in the beginning. It's not like there is some critical balancing point where everything has to be exactly right. I think some people get the wrong impression of what "balance" means in regard to planted tanks. Really, the only reason we need to limit CO2 and/or nutrient levels is for the sake of our fish.
Basically, CO2 and light level go hand in hand, and will compensate for each other to an extent because of the ability of plants to adapt (I'll spare the details.) If you have plenty of light, but not quite enough CO2, the plants might still be able to make full use of the available light, but this is not the "safe side", thus there's a greater risk of algae explosion. The "safe side" is to make sure there is plenty of CO2 (and nutrients of course), but not quite enough light, that way you ensure that light will be the limiting factor.
