It's interesting, because I've seen good arguments for both sides. Most fans think that AJ is one of the older mares of the Mane Six, but you're not the only one I've seen argue her being one of the youngest. You presented good evidence, but I'll go ahead and share my thoughts on your points.
1. Actually, Applejack said that she was "even littler than y'all." While AJ could be referring to age in this situation, she could very well be talking about size. It really isn't that clear. The reason I think she might be talking more about size is the fact that being a late bloomer was stated to be something that ran in the family in the Call of the Cutie episode. Granted, they were talking about being late to receive their cutie marks, but perhaps size was part of it?
2. I attribute Applejack's position in life more to the fact that she is supposed to be the quintessential family-centric character of the cast, so it makes sense to have her with at least one parental figure, and despite that, Applejack has consistently shown herself to be as much of a matriarch of the Apple family, if not more so than even that of Granny Smith. As for spending power, she's never been shown to be lacking it, she's just very business minded and does what she can to make the best profit. Farming doesn't exactly lead to a life of luxury, so if she seems poorer than Rarity it's probably because she is.
3. All very good points, but I think Applejack is slowly being groomed to take Granny Smith's spot. The thing to remember though is that while Applejack is very much capable of running Sweet Apple Acres on her own, she still has the utmost respect and admiration for her Granny. She probably doesn't want to take over until it's the right time, and for all we know that could be when Granny passes.
4. This is a really interesting case. Unfortunately, I think there's too many plotholes in the show to know for sure. When Applejack left the farm as a filly, Apple Bloom was nowhere in sight, which leaves us to wonder if she was born yet and if so, where she was. The growth rates of the ponies is also unknown, so while these points are interesting, I don't know if there's enough clues to come to that conclusion. Rarity could simply have grown quicker, or maybe Sweetie Belle is a bit younger than Apple Bloom. Seeing as she's the de facto sweetheart of the CMCs, it isn't unreasonable to think Sweetie is the youngest, even if they're in the same class. That being said, I CAN see Rarity being a year older than Applejack just as Fluttershy is to Pinkie Pie. I think most fans acknowledge Rarity as being one of the eldest.
5. I can't really put much stock into what Trixie says. She likely said that to make Applejack feel small and inferior to fire her up. Applejack later calls Trixie "missy" which is just as diminutive. I don't think age was being alluded to by either pony.
I tend to headcanon Applejack as being one of the three older ponies along with Rarity and Fluttershy, and this is mostly going by maturity level. I believe Twilight sits in the middle (4th to be precise) simply because that seems like a happy medium for the lead character. I could be wrong though. Glad to see another thought-provoking topic from you, A Talking Dragon. Been too long.