With regards to question/statement 1: I believe what you are seeing are items in 'your library', as opposed to 'the gallery'. 'Your library' shows any households or builds that you have saved to your library (just for you to see) and/or any households or builds that you have uploaded to the gallery (for others to see and download). If you delete something from the gallery, other players will not be able to download it, but it will still appear in your library until you choose to delete it from there. Your library can act as a way of transferring households or builds between different game saves for example, or if you build a house on one lot, but want to move it to a bigger lot.
With regards to question/statement 2: I've often found that I need to really double check what I'm entering. Make sure that I've selected to search for EA IDs (rather than hashtags for example). Then make sure that the name is typed in correctly (I'm quite bad at copying an EA ID from somewhere and including random spaces either side). Then I double check that the 'maxis curated' box in unchecked. often I uncheck it, hit search, don't get any hits and then find that the box is checked.