Primarily, the court is only going to care about what you did, not what the officer did. While there are issues that can be challenged that do have to do with the officer, the court will focus on the charge against you. However, keep thinking about these issues, you might find a winner. Also, there is no requirement to show the radar gun, as the court will basically rely on statements of the officer as evidence of what the gun read, etc.

YES, the police can park wherever they want when operating radar.

Short answer is this: the way the officer was parked will have no impact on your ticket.

This is not much different from an officer parking on the side of a highway or underneath a bridge when checking speeds. Though a civilian would not be able to get out of their car and watch traffic without a valid reason, the officer is lawful in his actions as he is carrying out his duties. Regardless, his parking will not impact your case unless the way he was parked/driving his vehicle impacted his ability to track your speed. It does not sound like this is the case.

Regarding the radar, you will never see the radar speed as it does not remain on the screen. That is not at all unusual.

I have had success challenging speeding tickets by focusing on the speed survey done on a road determining whether or not the posted speed limit accurately reflects the results of the speed survey. It is a technical argument and you would want an experienced attorney to handle it for you. It would depend upon what vehicle code you were cited under, however.

Good luck!