Can a Mac be operated by a iPhone

A Mac cannot be operated by a phone.

You appear to be using an iPad and an iPhone that are signed into a different Apple ID Account than the Mac. If they are using the same Apple ID, then they can sync your contacts, calendars, photos, music and files between the two.

If you want your Mac to have access to those same files and share that synchronization, then you should use the same Apple ID Account on the Mac, too. In fact, typically the best recommendation for someone who has multiple devices - iPhone, iPad and Mac - is to use only one Apple Account on all devices. Managing multiple Apple Accounts can be a bag of hurt.

There is no easy way to synch devices having multiple Apple Accounts.

Manage and use your Apple Account - Apple Support

Sorry, your question is not clear at all.

An iPhone and an iPad can sync messages and photos if they are using the same Apple ID for iCloud or fo Messages independently.

Not sure what you mean by "access a Mac from my iPhones and iPads".

A Mac is a computer, you access it by sitting in front of it and turning it on.

With that said, not sure what exactly you want to do about your phone and iPad on a Mac though. A Mac will not do anything about syncing messages and photos directly.

I would verify what Apple ID you have logged in for Messages, Face time and iCloud on each device and make sure it is actually different.

... they have different Apple IDs

Apple Account/Apple ID is intended to be a USER identifier, not a device identifier. Having different Apple Account/Apple ID for different device denies you many benefits of the "Apple-verse."