1. Please be quiet and draw you attention to me.

2. Please be quiet and pay you attention to me.
(Can we use 'pay' instead of 'draw'? Do you have some other similar verbs?)

No, "pay" and "draw" don't mean the same thing here. This is the correct phrasing for this idea:

Please be quiet and pay attention to me.

Other ways:
Please be quiet and focus on what I'm saying.

Eyes front!

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Draw:

The woman in the red dress and flashy jewelry draws attention to herself.

The beautiful scenery in that part of the country will draw many visitors.

http://www.onelook.com/?w=draw&ls=a
Take a look at all the different meanings for "draw" in the box at the right. Click on "more" for the ones you need more explanation/examples for.

1. Please be quiet and draw your attention to me.

2. Please be quiet and pay your attention to me.

Yes, you can use the verb "pay" instead of "draw" in that sentence. Both verbs convey the idea of focusing or directing attention towards someone or something.

Here are some other similar verbs you can use in this context:
1. Give: "Please be quiet and give your attention to me."
2. Direct: "Please be quiet and direct your attention to me."
3. Bring: "Please be quiet and bring your attention to me."
4. Attract: "Please be quiet and attract your attention to me."
5. Shift: "Please be quiet and shift your attention to me."

These verbs can be used interchangeably depending on personal preference or stylistic choices, but they all convey the same underlying meaning of asking someone to divert their attention towards you.