What you are describing is pretty much 'typical' sun conure behavior. I don't mean typical as in it should be accepted, I just mean its pretty common behavior.
There are several ways of addressing these issues. The first is you leaving the room. My Skittles is free-flighted and out of the cage whenever I am at home. I just let him follow me wherever I go since I don't mind it. BUT, that is MY situation and not everyone has such an isolated lifestyle.
You could try reassuring your sun before you leave the room- thats what I do when I have to leave the apartment. I talk to him while I'm getting ready and then I put him in his day cage, turn the music on and then head out. As I am heading out I reassure him again and he is fine while I'm gone. Doesn't scream as I walk down the hallway outside the apartment.
He DOES however start screaming as soon as I walk in the door. I usually let him out shortly after I am home but if he gets too noisy I will wait a bit. He'll usually comply and be patient. He KNOWS he will come out shortly- if I somehow changed the routine, he'd likely not be happy.
The biggest problem I have had is with the telephone. He does NOT like it when I am on the phone. Nor does he like it when I am on my tablet or on the PC. BUT, I found a way to make it 'acceptable' to him. I will look at him and pet him while I'm on the phone, basically give him some attention as well. By doing that, he is usually pretty good when I'm on the phone. Looking at them and talking a little bit on a regular basis goes a long way.
Maybe you could try talking to him while he's in his cage and you want some alone time with your significant other. If it still poses an issue, you could try covering him up when you want some alone time. Provided he doesn't stay covered for hours on end. lol.
For me, I just integrate Skittles into whatever I am doing and I have had very few problems since. But prior to that, when I was not paying him enough attention, he was a major "PITA".
Bottom line is, suns are VERY social creatures and require a LOT of attention as a result. You also want to make sure that everyone who you are going to have over on a regular basis are properly socialized with him. Otherwise, he may see them as a 'threat' to you and to his bond with you and proceed to 'attack' them. They can become VERY territorial if you don't set up strong and persistent boundaries.
You want to accommodate his needs, but you don't want to have bend to his will whenever he desires. He needs to know that YOU are in charge of the flock and not him. He WILL try to rule over you, just don't let him. Trust me, it can easily get out of hand. Do NOT underestimate their intelligence. They are sneaky and manipulative little buggers. BUT we love them nonetheless.