Wow!!!!!!! Ok so my problem must be user error! Here's a castle photo with my iPhone 7-
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Here's what I really want to correct even more than that- FIREWORKS!
My photos from my iPhone 7..even when the 7s comes out (I'm sure) do not get clear, sharp, photos. Especially from our room.
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The Olympus is going to cost me around $800 after accessories.. and I still need either the GoPro Hero Session, or a generic normal sized GoPro and accessories.. so for a 3rd camera I would want to be $300 or less. I had a DSLR, Nikon when my kid was a baby.. I left it in a stroller when we walked away while at a zoo, and it was stolen . Haven't bought another camera since, and don't really want to deal with lugging a DSLR around again.
Forget action shots with cell phone cameras (unless it has a "sport shooting" mode). The blurriness in the background (second shot) was because you must have moved the camera. As I said before, the camera recognized the dark scene and kept the shutter open longer. If you moved the camera during that time the result is blurry photo.
Fireworks shots will not get too much better unless you have a tripod or other stable object and know how to take them. I've taken many long exposure shots on trashcans, railings, shelves, etc.
It's not rocket science but it does require an advanced knowledge of how your camera settings works and how to manipulate the exposure triangle.