THREE RHYMING RIDDLES

1)
Round and round the earth I go,
I do not move - not fast or slow;
I have no beginning, neither an end,
North and south do I blend.

2)
Without a partner, I sit here mutely,
This loss I feel, most acutely;
My grace and beauty all may reckon,
My promised voice to you may beckon.
But I must wait the gifted hand,
Whose touch I welcome as my command.

3)
You can do this in a tub, to get yourself clean,
You can do it to curtains, to stop being seen;
You do this when you can't even guess,
You do it when you're equal in chess.
You may do this to get pictures of people and things,
But then you must use either pencil or pen.

Answers:

1. Equator
2. Musical instrument 

3. DRAW:

Draw a bath
Draw curtains
Draw a blank
A draw in chess is a tie game
Draw pictures