Which version of Tropy are you on? The items in the project table/grid used to be square (the images were cropped) but since 1.6 they should preserve the original aspect ratio without any cropping. Note that when you first open an existing project in 1.6 it may take some time for all the thumbnails to be re-generated, but it should happen automatically; if not you can try forcing it by consolidating the item in question.
The issue of the same photo belonging to more than one item is annoying, true. To copy a photo and pull it out of an item (i.e., leave the photo as part of the current item and create a new item with the same photo) you can right-click on the photo (in the panel) and use the Duplicate Photo action (you can then drag the duplicate to another item). Currently, Tropy makes no copy of your original photo (for most formats) so duplicating a photos will not require a lot of extra space on your drive (we currently do duplicate the thumbnails though). Since you’ve duplicated only the photos (not items) you don’t have any excess clutter at the top level. But yes, this is all a trade off: once Tropy allows better searching/analysis within an item it will give you the option to use a different metadata granularity, rather than duplicating photos across items.