Does it matter which direction I circle my hand?
The standard motion is a clockwise circle from your own perspective. However, as long as you are making a clear, continuous circle on your chest with the 'S' handshape, the meaning will be easily understood.
How do I show that I am *very* sorry?
To emphasize your apology, make a larger, slower circle on your chest. You should also match this with a strong facial expression, perhaps lowering your head slightly or furrowing your brows to show deep regret.
Can I use this sign to say 'excuse me'?
No, 'sorry' and 'excuse me' use completely different signs in ASL. 'Sorry' uses an 'S' handshape on the chest, while 'excuse me' involves brushing the fingertips of one hand across the palm of the other. Use 'sorry' only for actual apologies.