Q: Help! Recently bought a MacBook Air and noticed strange glitches, what do I do?

I recently bought a MacBook Air and as of the first day I noticed a few things that didn't seem right. Initially, I bought a new laptop because my old MacBook Pro was running too slow.

A few red flags happened with the Air:

When I first received my new computer, I tried using the AirPlay on my TV but nothing would project onto the screen of my TV (TV worked with other devices). I also noticed that when I would unplug my laptop after it fully charged, the battery would still say it was at 100% even after using it for a few hours. Additionally, it has a hard time loading web pages and will stay loading for minutes. Over the past few days I've tried clicking on tabs to no avail (nothing happens when I click on links).

Could something be wrong with my new MacBook? If so, how will Apple fix the issue?