Two Charades

My first is no proof of my second,
Though my second's a proof of my first.
If I were my whole, I should tell you
Quite freely my best and my worst.

One clue more: -- If you fail to discover
My meaning, you're blind as a mole;
But, if you will frankly confess it,
You show yourself clearly my whole.

II
How many authors are my first!
And I shall be so too
Unless I finish speedily

That which I have to do.
My second is a lofty tree
And a delicious fruit;

This in the hot-house flourishes--
That amid rocks takes root.
My whole is an immortal queen
Renowned in classic lore:

Her a god won without her will,
And her a goddess bore.