I brewed my first barleywine in early December. It is not an American-style, rather an English Barleywine. While I don't anticipate it being done conditioning until mid-June, I have sampled two bottles over the last couple of months, and it is my best brew to date.
The recipe I came up with is roughly inspired by the Fuller's 1999 Vintage Ale from Clone Brews. Basically, I worked it in BeerSmith until I came up with something I liked. Part of what I did was add light brown sugar to the wort after flameout. For a five gallon batch, I added half a pound. To understand the flavor changes, I did taste the (cooled sample) of wort from prior to adding it, and one before racking. The flavor changes are subtle, but there. Once it was ready for bottling, I used 75 grams of light brown sugar for carbonation. I was shooting for a fairly low carbonation volume, as well. The brown sugar added after the boil did what I had read it would do. It imparted slight sherry and raisin notes to the beer, which is a characteristic of an English Barleywine.
That being said, I would think that the addition of table sugar would serve to boost the starting gravity and provide more sugar for fermentation, but I do not see it imparting any additional qualities to the finished product. I am not sure if that is your intent or not. My only experience with an American Barleywine is with Brooklyn's Monster Ale (which I was not a fan of) and Smuttynose's Barleywine Ale (which I quite liked, mostly due to the similarities to an English Barleywine).
As to the specific questions you ask, let's start with the total percentage of sugar in the recipe. Way back in 1998, BYO did a style profile for Barleywine. Considering the age of the peice, it is fair to assume that it was specifically targeting English Barleywines at the time. They state that up to 15% of the total fermentable sugars could come from directly adding sugar. I will try to hunt down the reference, as I did not seem to put a link in my notes, just the date and a few quotes from the profile.
I add the sugar at flameout for the purpose of having to use less hops, as the isomerization is more efficient with lower sugar levels in the wort. I probably could have shifted some of the extract I used to flameout, as well. Additionally, I feel that adding the brown sugar at flameout helped to carry those subtle notes I was looking to add. A smaller test batch where I had added the sugar up front ended up missing a lot of the subtlety that the post-boil edition seemed to preserve.
For fermentation and conditioning purposes, I used my fairly standard "68 degree" model. As that is where I keep the thermostat this time of year, and it is within range of my yeast, that is just the norm. I am going to need a fermentation chamber in the next couple of months, but that is another story. I primaried for four weeks and then bottled. Bottles are currently stored in the same general area, so it is going on three months at 68 degrees. Within the next month or so, I am going to cellar the beers, where my basement stays at a fairly constant 58 degrees until the middle of summer. As to long-term storage, I would aim to keep it cool, probably no warmer than 60 degrees, if possible. I have nothing to back it up, but I would imagine that it would help to sustain shelf-life if you are planning on cellaring for an extended period of time.