1. That arrangement isn't similar to Amazon Fulfillment at all from a legal perspective. Best Buy is just using the warehouse fee as a gatekeeper to filter out low-value/low-scale products. They have limited shelf space and relatively low turnover. Best Buy is in the business of selling products in its stores, but not in the business of marketing them unless they're the type of products that bring people into the stores (i.e., doorbusters). They rely on the product makers to do the bulk of the marketing, especially for new products where demand is not known. Key factoid: they refund the warehouse fee if the product actually sells.
2. Yes, but it's not comparable. Amazon isn't being investigated for competing against the likes of Champion or Under Armour. They're being investigated for competing against third party sellers (which might or might not be their own brands) by promoting their own products against their competition.
Again, you don't seem to understand this basic point: the product maker's income comes from Amazon buying the product, not the end customer. If Amazon launches a white label brand, that's not an antitrust violation on its own. It's also fine to use data from selling Product X to sell the white label brand. Antitrust law rewards competition. It's even fine for Amazon to promote their own products over competing brands, since those brands have other sales channels they can use and they've already been paid for their product or are contractually obligated to get paid for their product.
The problem is when Amazon promotes their own brand over other products in unfairly competitive ways, such as in search results for those competing brands' products. (Example: if searching for Lululemon brought up Amazon's peak velocity as the first few results). This is still a weak example of antitrust because Lululemon's already been paid by Amazon. But if you replaced Lululemon with Cococyle, an upcoming brand that sells through Amazon's marketplace, you'd have a clear antitrust violation.
3. There is a competitive concern here because these retailers control shelf space and promotional material and uses their physical retail space and sales data to compete against brands. Walmart more-so than all the others.
No, false. There is competition here, but it's not unfair competition because the brands have already been paid for their products. Also, the brands have a very strong defense: they can simply pull their products from the store. (This strategy has actually been used many times to fight off store brands and it's the reason store brands and generics are given lower-shelf placements.) Most people go to grocery store for the branded products, not the white label products. TJ's is pretty much the only store on your list where they opposite might be true.
Again, for emphasis: competition is fine. What matters for antitrust is unfair competition, and none of the stuff you've cited is unfair.