A bit late in arriving, but couldn't stop myself from responding to this thread.
(1) How old were you when you first listened to Leonard?
This reply is a combination of me (62) and my son (20 months). Yeah, yeah, I know.

I first learned of Leonard when I was dating a student at the University of Bristol, 1968. An American, I was stationed in England at the time. Have been a fan since.
I have a couple older kids, 23 and 29, and they are major Cohen fans, but my youngest got hooked when he was only 8 months old. Really.
I'm a stay-at-home-dad, so introducing solid foods fell to me, and I would always put on the Field Commander Cohen Tour CD while feeding. Then, to entertain my son, I started playing "air violin" during Raffi Hakopian's solo in "The Window." Soon, my son was also playing air violin.
For several months, he would not eat unless the Field Commander was present. Then, we branched out to other albums and then YouTube gave us visuals. Though he loves Pavarotti and Heifetz and Mozart and Pink Floyd and Dylan, et. al., Cohen remains my son's favourite. Now that he speaking, he proudly tells everyone that "Leonar Coen" is his favourite singer.
(2) How much did you understand of the sexual/violence references?
My older kids and I pretty much know it all. I'm a literature major and retired writer, and after figuring out Eliot, Cohen was not that tough. While some of the lyrics can be a bit of a challenge, I find that meaningful differences in interpretations usually arise based on my mindset, not the lyrics.
(3) How did hearing these lyrics cause you to feel?
His work has been very liberating for me over the years. It's nice to know someone feels almost exactly as I do. With Dear Heather, I was prompted to provide the lyrics to my wife with a note saying "He continues to write my life's story."
(4) What age do you feel would be the most age-appropriate for children to first listen to Leonard?
Cohen's work is perfect for all ages. Even my toddler. Now, my boy doesn't understand the complexity, and he doesn't understand the simplicity. He just likes the sound. This music will be a great tool for teaching, for as he ages, we'll unwrap a new layer of meaning every once in a while. Since I still find new joys in the old songs, I will have given my son a constantly changing tableau that will comfort him throughout his life.
(5) Should parental- or adult-guidance be a part of these initial listening experiences?
Guidance? As in controlling or hiding or denying something? No. Help in understanding poetry? Well, sure. We all need help with poetry when we start, and though I "know" poetry, I find it essential to consult references, attend lectures, sit in on a university class or two, read the critics, etc.