Yes, "rather have had" is correct English. OTHER EXAMPLES: My father bought me a car, but I would rather have had a motorcycle. I would rather have had a blue blouse, but the only color they had was red. I would rather have had a small wedding, but my fiancee wanted a large lavish one. I would rather have had the surgery rather than deal with all these painful treatments.

Yes, it's perfectly correct. It's a type of 3rd conditional, that is, an alternate reality in the past. If you're really interested in these structures, you will definitely want to read (and comment on) my popular mini article, "Grammar boost: Conditionals cheat sheet PART 1": https://www.italki.com/discussion/164505

Yes it is correct. It means I would like to have [in the past] one breath of her hair, one kiss of her mouth, one touch of her hand than to live an eternity without it. Just one If you could give a link to the video and the time it appears in the film people can give you a better answer.

Yes it's quite common to use that sort of phrase. You can also contract it by saying "I'd rather have had". Also, watch out in everyday spoken english how much further native speakers, specifically in the UK, can further contract such a sentence. You might hear something like "I'd rather of / 'av 'ad" which is grammatically incorrect but they're just saying it so fast that it sounds like that.

Yes. I have watched that movie too. Since the guy used to be an angle who couldn,t feel things but wouldn't die ,and in that part the woman he fell in love with was dead and another angle was asking if he had known that she was going to die so soon ,he would have decided to turn into a human or he thinks he made a mistake to let go of his eternla life as an angle. With that sentence he expressed that he has no regrets since just one kiss,one touch and one breath worth more than living for an eternity. Nice movie,by the way!