What makes tab or sheet music to be illegal

I've come to understand the following:

• Distributing printed sheet music that is for sale and/or copyrighted is not allowed.
• Hand-copying sheet music is allowed (for personal use only?). I don't know how this applies to lyrics, but it seems normal to see hand-typed lyrics on (legitimate?) websites.
• Arrangements are copyrightable---even if the original melody is in the public domain.

Thus, it should not be illegal to transcribe chords, tablature, and possibly lyrics by ear. Distributing original copies is not allowed. There are also gray areas: "If you can't tell the difference between lyrics transcribed by ear and lyrics copied from a book, what is the difference?" I don't know! However, I'm sure there's a good answer to this on the Web. Let's see if we can dig it up! (Edit: The thread you linked provided some answers.)

Edit: For your second question, do you mean "record your own cover of a song"? If that's what you mean, I certainly don't think that is illegal. You see it all the time. Commercial use, however, is definitely not allowed without permission.

Suppose: You are an amateur performer; you record a cover of a popular song and publish it on the Web. Suppose you record several popular songs, and over time you achieve some recognition (intentionally or not!). Your recognition now allows you to sign a deal with a music publisher, and you find yourself earning a living (or more) publishing original music. Now the copyright owners discover your story. At this point, their entertainment lawyer(s) have a good case that, without the material that gained you popularity, you would not have earned what you have now. Thus they could expect a settlement for the royalties the copyright owners would have otherwise received.

I think it is a bad idea to approach ethics with the mindset, "What can I do while still not breaking the law?" Instead, simply consider "Is what I'm doing is fair to the copyright owner?"