Very often would and could are used not to express possibility/capability but to express willingness to do a thing. It is a polite way of asking.
If you could get me a beer, I'd be much obliged.
Obviously, anyone who can walk to the fridge could get you a beer, but you are asking whether the person is inclined to do you that small favor.
So the statement
I would do B if you could do A.
more likely means "I'd be willing to do B if you'd be willing to do A." And it's nothing to be worried about.
Addendum (Responding to the OP's comment question)
Specifically, you can't apply mathematical strictness to human language. If you look at my profile, you'll see that one of the quotes I cite is Frank McWhorter's keen observation that "no language makes perfect sense."
Much of what happens in language, especially speech, is rife with overtones and undercurrents and connotations; very seldom is it the strict chop-logic imparting of fact. You know this is true, for without that overloading of meaning how could something like irony exist? Example:
You say a person can't use two affirmative words to express a negative? Yeah, right.
"Yeah" and "right" both represent affirmations. And taken together they can also be an affirmation. But said skeptically, they can mean the person speaking the words doesn't believe whatever he's being asked to believe. It can be a very emphatic way to say "That's not true at all."
Math is clean, pristine, beautiful; human language is messy, murky, and also beautiful. You just have to understand that they're beautiful in different ways.
Yeah, right. (And I mean that in the positive sense this time.)
Best Answer
"If you went to bed earlier, you would not be so tired." to me means that someone is consistently going to bed too late and is now (or usually) tired because of it.
I would interpret "If you had gone to bed earlier, you wouldn't be so tired." as more of a one-time occasion where someone stayed up too late and is now tired as a result.
On your second question, "If you had gone to bed earlier, you wouldn't have been so tired" sounds better to me.