Can my property management do this?

They let you know they were coming in writing so that covers the law........ in so far as letting themselves in, they can, but very rude to take a photo of you in bed... maybe a 'newbie' who has no manners and doesn't respect tenants....you can always complain to the office about the lack of respect shown, depends on what the agency/landlord is like, maybe none of them respect other people or privacy as most people if they found you in bed would apologise/closed the door and say they will inspect the rest of the place while you got up

The only time they can enter your apartment without your promission if they smell gas.

Yes entering with proper notice given is legal. Knocking is polite & is usually done out of courtesy but not technically required. They do not have to specify why they are entering in all states. You failed to give a location so you will have to check the state specific laws on that.

Taking pictures of the unit is legal.

Taking pictures of you sleeping is creepy. While it seems like a no brainer this may actually be legal. Should be illegal and actuality are not the same thing. This would not be covered in landlord/ tenant law. You would have to check general laws to see if that is actually illegal or not.

Yes, they can do that and they did. You were given notice, despite that they did not have time that specific day or time. There is no requirement that you be home when they inspect and they don't know that you are sleeping. In fact, they don't even care. They are there to do a job.

The landlord or his agent is only required to tell you that they are coming in advance. They don't need to reveal the specific reason. They fulfilled their obligation.

Your sleeping through the alarm and the knock at the door is on you.

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If there is a Tenants rights group in your area contact them. In general I would think that is not a proper notice. In addition the laws in many places should be updated to require them to knock and call before entering. Taking pictures of you in bed is not acceptable or legal in many places.

Just because you didn't hear the bear poop in the woods doesn't mean the bear didn't poop.

Oh sure your alarm randomly malfunctioned and of course they didn't knock before they entered your apartment and bedroom. That must be it because I've never ever heard of anyone sleeping through things.

How on earth could any of the other tenants testify as to what happened in your apartment? Were they there? No. But you were...albeit asleep in bed...so you're not a very good witness.

To answer your question....yes they can (but they probably didn't).

Yes - they can do this.

They probably knocked and you didn't hear it. I am a landlord, and I've never been with a property manager or agent that doesn't first knock.

If your alarm "didn't go off" it's because you didn't set it. Unless it somehow broke and stopped working overnight.

Bottom line - They notified you. You got the notification. You failed to be "ready".

I think you lose this one.

Depends on your laws and the small print of what you signed, but if it's for fire or utility safety they can almost certainly come in at anytime.

You may need to bypass the property manager and contact the actual owners as it doesn't seem reasonable for a routine inspection.