You have a few different questions. 

HDMI Output, the resolution may be higher than the monitor or TV you are connecting to. You can access the recorder from the network and make the Display change. Here is a video on how to diagnose and fix this issue.

The beep and restart show that either the Motherboard is bad, the hard drive, or the power supply. The most common is the hard disk drive; open the unit while off and disconnect the SATA and the Power to the Hard drive, turn it back on and see if the recorder completely boots up with no issues. If it does then your third question would not apply here as the drive is faulty and you would not be able to backup your footage, there is also no accessing the data other than with the drive itself. 

If its the Power supply, replacing the power supply will help, if it's a built in power supply then its rare for those to go bad when it comes to them not providing ample amperage, if its the motherboard, there isn't much you can do there, you could get the same series recorder and place the drive there and see if you can get the footage in this manner.