"Could I leave the anhydrous CuSO4 out in the open for a while until it attracts the natural H2O in the air? Would that form Copper Sulphate?"
You are missing the point - anhydrous copper sulfate is still a copper sulfate. If you want to make a distinction you have to list the with their full names, which you didn't. What would be formed is not a "copper sulfate" but "copper sulfate pentahydrate".
Still wondering how I would determine the difference between CuSO4 and CuSO4.5H2O via chemical analysis, like titration or something.
First of all - it is enough to look at them, as they are quite different (which we told you several times).
Analytically there are many ways of determining how much water is in the sample. You can weight it before and after a roasting, as roasting removes water. You can weight the sample, dissolve it and titrate to check how many moles of copper (or sulfates) are present, then calculate amount the amount of water from the difference. You can try the latter approach but with any method that allows the determination of the amount of copper/sulfate (like spectroscopy).
Why does the CuSO4(a) pick up so much H2O just by sitting idle? If that was the case, then why isn't my stash of CuSO4 crystals turning into CuSO4.5H2O....OR is it?
Copper cation has a great affinity to water molecules. Every sample of anhydrous copper sulfate tries to get water from the air. Depending on the humidity it will absorb water up to becoming pentahydrate (what we call pentahydrate rarely contains exactly stoichiometric amount of water, it is typically a bit on a dry side). Your anhydrous sulfate does absorb water, just - if it is kept in the closed jar or bag - does it slowly. Leave it open and the process will speed up.
So, I've heated CuSO4.5H2O and made CuSO4(a). it's slowly turning a to a sky blue, as it's picking up the H2O. When is it sufficient to say it is just CuSO4 and not CuSO4(a) or CuSO4.5H2O? And can someone please explain what I should study to learn how to verify this myself thru some sort of analysis. Thank you for the replies.
Again - asking "when it is just CuSO
4" is meaningless. Sometimes it is an anhydrous copper sulfate, sometimes it is a copper sulfate pentahydrate, sometimes it is a copper sulfate tetrahydrate, sometimes it is an unspecified hydrate - but at any time each of these can be called "copper sulfate", so it is a copper sulfate all the time.