How to check if my iPhone is being hacked?

Why do you think your iPhone was hacked?

No, if you haven't jailbroken your iPhone, it's not possible.

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If you think your Apple ID has been compromised

If you think your Apple ID has been compromised - Apple Support

See who has access to your device or accounts

See who has access to your iPhone or iPad – Apple Support (UK)

Personal Safety User Guide

Personal Safety User Guide – Apple Support (UK)

you could download a free antivirus from the app store.

Most antivirus apps for your iPhone aren't really designed to find viruses. They are often security programs that bundle multiple functions to justify the price asked. It is quite difficult for security software makers to make a really good antivirus app, because Apple has pretty much boarded up the system.

I agree with you, but some antivirus apps are able to track whether or not youre router or ip adress is compromised, and if it is, then any device connected to that network could pottentially be hacked.

To check if youre phone is hacked, you could download a free antivirus from the app store.

It is actually possible to have youre Iphone hacked without jailbreak.

It may not be a severe one but websites could be able to access your calendar and send spam reminders for example

That only happens if you allow it to add to your calendar, which isn't really hacking.

No, because some websites find ways to access youre calendar without permission, and then that would kind of be considered as hacking.

Have you jailbroken you're phone or download a suspect file?