"There is more to life than basketball" is something you might say to a child or friend who is obsessed with basketball and can only talk about basketball. You are telling them there are other things they can spend their time on, there is more to life than basketball. Another example "there is more to life than work" is something you might say to someone who thinks of nothing but work. Hope this helps!

there's more to it than meets the eye......there's more to a situation than what you actually see or aware of

First two are correct. Last one is still the same -- "There is more to the skill than the learned technique" = to master the skill you need to know the learned technique but also other things. For example: "There is more to speaking English (the skill) than grammar (the learned technique)." = to speak English well you need to know grammar but that is not enough. You also need to practice a lot!

I think the confusion is that this is not a comparison of objects in the same class. In the sentence "there is more to x than y" you are saying that y is part of x, but that a lot of other things are part of x too (a, b, c, d, e and f are also part of x). Does that help clarify?