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#1: as you noted, you can ignore those errors. For completeness, there's background in a previous forum post.
#2: you might be trying to access a widget's store directly. Try getting a reference to the store, then running your query on that.
#3 sounds like an app specific CSS issue. If you can post a repro, we might be able to help.
#4 sounds like it's not something you need help with but rather that things are working as expected.