I sympathise. My twins are pretty canny at picking up when I'm leaving them and it can be very difficult to reassure them, though luckily places like bed and nursery are OK.
My reaction to your post was that you may be feeding his anxiety by projecting anxiety of your own. If you seem unsure about your action (going out of the room/getting out of the car etc) then he will pick up that there's something to worry about. Your nervousness is understandable because you're bracing yourself for his reaction, but it could be feeding into a cycle of anxiety for him.
Try this at bedtime: if he is upset when you tuck him in, go through a little routine with him of naming all the favourite toys in his bed, look there's your teddy, what a cosy bed you've got, bet you can't wait to snuggle up and get all comfy, your brother looks happy in bed doesn't he, bla bla. All quite soothing and upbeat. Then say mummy's going downstairs now but I'll come back in one minute. Then leave the room, wait precisely one minute (whether there are tears or not) and go back in. Then it's night night, reassure reassure, mummy's going downstairs now but I'll come back in two minutes. Then do the same. The intervals are 1, 2, 5 and 10 minutes.
I had to do this a while ago when my son went APE every time he went near his cot. I never had to say a word to him when I went in after the 10 minute interval, because he was asleep by then. Quite quickly I was able to stop it because he had learned to trust that I was close by.
If he's OK going to bed but wakes in the night, I would do the same trick again but you will probably be worried about him waking his brother. He might do - probably will in fact - but in my experience, the one who was asleep beforehand is quite keen to return to that state so if he wakes you can quickly resettle him and then focus on the 'spaced soothing' with your eldest.
Do be prepared to find it hard and feel like caving in and trying some other tactic, especially at 3am, but be consistent and it will work. Besides, you have to help him fix his sleep for your own health, so try it and stick at it.
As for the other situations, try not to worry about his reaction or let it show in your voice when you go away. Don't rush or seem flustered, and when you return treat it as completely normal that you've returned even if he's going loopy. No need for extra cuddles because you came back like you said you would...hopefully if you can avoid him feeling that something bad has just been prevented, he'll get more relaxed about you leaving his side.
Sorry, bit of an essay but I hope things get better for you soon.
Ever since me and my ex p separated last may my then 3 year old and now 4 year old has had really bad seperation anxiety. He doesn't sleep at all well and always comes into my bed at night. I can't go into the petrol station alone as it all kicks off, trying to go out in the evening is a nightmare. I've tried to explain everything too him but the problem seems to b staying and I'm really at the end of my tether. It's probably worse as I give into the night time stuff but sometimes I literally get 3 hours sleep a night and its killing me. Probably should of mentioned I have a second son who is 2. Anyone else dealt with this????