This is my take on this one:
I would like to have written the third love letter, because it´s simple and yet beautiful.
I would like to have written the third love letter, because it has a pretty, old-fashioned, but beautiful ring to it.
1) There was not much to change as it was, but the slightly repetition of the word "letter", at the second time we already knew that you were talking about a letter/letters.
2) These are just two ways, among several that are likely to come.
3) You do express yourself in English, the "touches" here are meant to enrich your vocab and to convey it in a more natural English (or close - we all have limits). Again, as I pointed out, you are in the right path.