The tiles change as you do things. Each time you open a book, the tile for it is put onto the home page. And one is probably pushed off to make room. Same happens for all the other things you can do.. If you dismiss a tile, the tile that was most recently pushed off, should return.
There are two special tiles. The first is always the book you most recently read. If you dismiss this, it is replaced be the next most recently read book. The second tile is the sync tile. This cannot be dismissed using the UI. But, you can get rid of it with my Kobo Utilities plugin in calibre. And prevent it and most other tiles from returning.
I don't use the alternative readers, so can't answer the other question.
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