That will work perfectly, the camping is minutes away from most of the hikes

To prevent "squatting" typically you must occupy a site the first night of your stay, but you should have no issues if you are occupying the site at night and away for the day.

Technically, yes. You write the day of your departure on your portion of receipt and post it at the site. That being said, I have watched someone pull into an empty site without checking the post. To avoid confrontation I suggest you leave camp chairs or something of low value to make it obvious you have the site. Rangers do check the park. Good luck.