Is it possible for a hacker to hack your iPhone?

Can they hack into your iPhone and find out your location, name, recent searches, etc? Is that even possible? Can they turn on your camera? Hack your messages?

Not necessarily your actual phone but they can sure find your location.

If they can get a hold of the iphone and they have a software for it yes. If they don't have your phone nope!

don't worry keep your phone close

Your precious can be hacked like any other device on the internet. Direct hacking is possible by finding exploits in the Wi-Fi firmware (if connected via Wi-Fi), the bluetooth stack and the GSM firmware (via SMS, GSM signaling). This is extremely difficult, although exploits are available to a handful of people. But they are Way too expensive to use them against "normal" people. Hackers want to make money, not impress people by spending all their money. And widespreading them will lead to patches so the precious exploit is gone.

The indirect way is through applications. Although Apple does monitor the code inserted by apps, exploits are found regularly. They are not published because Apple doesn't want their users to be scared (or informed), but they are fixed in ios and app updates. So if you are using the apps they connect outwards and may be hijacked.
Once getting a foothold on the iphone, the hacker has to use privilege escalation hacks (exploits) to increase privilege to access e.g. The camera.
Due to the policy of information hiding of apple it is slightly more difficult to find exploits in ios, but it is much easier to use them as apple sedates its users with repetitive marketing slogans.