1. What issues of Dungeon does it go through? I know it just ended.
It started in issue #156 and finished in #175.
2. Does it tie into Red Hand of Doom?
Not really. The heroic tier takes place in the same valley, but the home base city is new and off of the left hand edge of the RHoD map). The first adventure kicks off in Brindol and a later heroic tier adventure makes a brief stop in Brindol. A visit to the southern wastes briefly mentions a RHoD character in the background notes. Other than that there's no explicit mention of RHoD.
I never played RHoD, so I can't say whether there's nods to RHoD that aren't explicitly called out.
3. Are there any articles in Dragon that tie in?
There was one that provided character backgrounds: "Characters of War" in Dragon 366. They're also in the Character Builder. I think that's all.
I played SoW through to the end of the heroic tier and I found it a bit... dull. It's linear in the extreme, both in terms of the adventures and how they're connected. There's no provision for events in one adventure affecting a later adventure. Nearly all of encounters are combat-oriented, nearly all of the adventures are a variant of the dungeon crawl, and there's a dearth of interesting NPCs and roleplaying notes. The adventures follow a predictable pacing pattern.
After a year and a half, I was sick of it. My players were still having fun, though. We've switched to War of the Burning Sky and I'm liking it much better after three sessions. Not sure what my players think yet.
On the other hand, SoW's combat encounters are excellent. They're all very well balanced and there's a lot of great set-pieces. I particularly enjoyed the start of SoW #1 and the end of SoW #2. If you plan to run it, I'd recommend cherry-picking the best encounters from each adventure and dropping the filler. It's also a good beer-and-pretzles game to play as a pick-up during another campaign... it's very easy to DM and doesn't require a lot of prep.