How do I regain control of my iPhone and disable remote access?

When you go to Settings > [name on top], is it your Apple Account you see there or someone else's?

What concerns me is that you said you paid hackers $500, which sounds like you may have entered their Apple Account into your device. If that is what was done, it was done by you and not remotely where you have to first remove your Apple Account and then enter theirs along with a Password that they gave you to enter. Doing that would turn control over your device to someone else. Is that what you did?

Why do you say that a Mac is controlling your device using Screen Mirroring? There is a Screen Mirroring feature using a Mac, but it requires the iPhone to be within Bluetooth range (about 30 feet) and permission must first be granted on the iPhone and can also be disconnected there. That feature does not work over the internet where your device can be remotely controlled.

Receiving an SMS Message, such as for Password resets for apps, is specific to the SIM on your phone provided by your cell carrier. The phone is still capable of receiving those even when there is not an Apple Account signed into the device. If you are having trouble receiving SMS Messages, then contact your cell carrier as they may need to reprovision your SIM/eSIM.

You can upload photos here, but just make sure it does not include any personal information. When you post, one of the options under the post shows a landscape icon (second from the right), and choosing that will allow you to select the picture to upload.

The most common way someone else can get your account information is by responding to a phishing message and providing that to them believing you are communicating with a legitimate person. NEVER click a link or call a phone number provided to you in an email/message and give out any personal information. Treat emails/messages as information only and for any follow up use known contact information, not one provided to you in that communication.

Recognize and avoid social engineering schemes including phishing messages, phony support calls, and other scams - Apple Support

If you feel an unauthorized person/app is remotely using, controlling or monitoring your device, then that is possible only if you have done one or more of the following Don'ts...

1. Don't hand over an iPhone to kids or to a stranger without Enabling Guided Access
2. Don't share Apple IDs
3. Don't Jailbreak
4. Don't share sensitive information pertaining to your device
5. Don't give in to Phishing
6. Don't plug in your device in Airports and Public places through third-party cables and trust the device. Beware of Juice Jacking. (Especially in India)
7. Don't leave your iPhone unlocked and unattended in public places like offices, schools, malls, etc.

If one of the above is true then quickly change the Apple ID Password and Return iPhone settings to their defaults.

If a person has ever had your passcode, they could’ve installed something quietly — so the full erase and setting up as new is the safest option. How to factory reset your iPhone, iPad, or iPod touch

Keep the iPhone updated to the latest iOS always and never Jailbreak. That's it.

iOS / iPadOS devices cannot be hacked or infected with Viruses / Malware / Spyware *** unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed them on your device, and/or have Jailbroken. 

It (Hacking) also depends on how careful you are in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password, etc with your friends and family members.

Be judicious when sharing the device's sensitive and valuable information with friends and family members.

**The primary reason for this is Sandboxing. All third-party apps are “sandboxed”, so they are restricted from accessing files stored by other apps or from making changes to the device. Sandboxing is designed to prevent apps from gathering or modifying information stored by other apps.

Security of runtime process in iOS and iPadOS - Apple Support

The sandbox on an iPhone is a security feature that creates a restricted environment for each app to run in isolation from other apps and the operating system. It is a core component of iOS's security architecture and plays a crucial role in making iPhones more secure.

If you doubt the authenticity of the information provided earlier, you have two alternatives:

1. Report the hacking incident to local law enforcement authorities and actively pursue the case.
2. Accept the credibility of the information; it is impervious to hacking. Just as some individuals hold unconventional beliefs, such as a flat Earth or moon landing denial, one has the freedom to believe in anything. The choice ultimately rests with you in this open and free world.