This is some great feedback.
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I think a search is definitely something looking into. The default Concrete search can be adapted to search for products, and output product details, but that does require a level of knowledge.
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This can be achieved now with product attributes and a custom product/list template
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Further options might be a good idea, but I tend to lend towards this being a customisation, rather than something built in. What might be useful are some semi-official additional block templates
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I agree the filters could be extended
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The cart appearance is another thing that I lean towards being a customisation. For example, with the sites we build with Community Store, we don’t actually use Bootstrap - we build them ourselves with Sass, so have full control over styling. That’s one of the core goals with this add-on, that’s it’s able to be styled and customised easily - but it’s not aiming to be able to handle a very wide range of styles out-of-the-box.
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This display comes down to styling again, but I think considering a further option like a horizontal list would be good
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This can be done now with attributes, or through fetching the stock level programatically. It does become fiddly though with variations.
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There currently are some reports that can show you the details of every customer that has purchased a particular product. Further reports to show customer details might come down to the particulars of the data you are wanting to fetch. I think such a report would be useful, but might be better handled in an add-on that installs further report pages.