Hi @jonc and welcome to SAS! These are great questions…
Amazon is inconsistent in how it alerts Sellers to possible category and product restrictions. As you have seen, sometimes a category will be locked with a 
icon–but sometimes it won’t be.
- Just because you can create a listing in a category does not necessarily mean that you are approved for that category, so you will have to make an attempt and see what happens.
- Sometimes you are approved widely for a category but not specifically for all product types (or brands) within that category.
- Sometimes you create a listing, make an offer, and even make a sale, before Amazon alerts you to any possible restrictions.
You can’t, really, but you can prepare yourself for handling them efficiently and effectively. A few quick tips:
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Since you’re going to private label, set up your company legally, register your trademarks, and secure Amazon Brand Registry before actually purchasing any product. And do extensive product research through multiple resources, not just one “do it all for you” company.
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Source your products from legitimate suppliers with legal clearance (per USA laws) to the product patent to resell to you for the purpose of private labeling. Just because someone sells it on Alibaba doesn’t mean they have legal rights to the design or product.
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Have all products sent directly to you from the supplier/manufacturer, for inspection and quality assurance, before shipping to customers or to FBA. When you private label generic products, you assume all risk and liability, becoming the de facto manufacturer. You limit your risk by in-person inspection and QA.
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If you’re going to use FBA, then only send a small stock of your inventory to Amazon at the beginning, while also selling FBM. This way, you’ll get a gauge of sales rate, how much you should send to FBA, and how much your FBA and storage fees might be. Plus, if there are any account or inventory problems, you limit the damage that FBA can do to your business.
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Save all documentation regarding all supplier, supply chain, quality assurance, and legal rights–including invoices, receipts, bills of sale, shipping information, trademark/copyright/patent documentation, product storage and packaging details, packing slips, contact information, testing, compliance, and more–and store it so that it will be easy to access and provide to Amazon when they ask for it…because they will ask for it.