Can the drain pipe in my bathroom vanity be turned to the side?
This shouldn't be an issue. With the standard P-trap, you can probably turn it so that it goes toward the side instead of towards the wall to get your 9". The important rule of drainage is that it always needs to slope down (other than the traps at each fixture) and that you can't get too far from the vent. Neither of those should be an issue with the change you're making.

Do be sure that the new sink isn't significantly deeper than your existing one since that could result in the drain needing to go uphill to get to the wall (which water doesn't like to do).