I think it’s just a deer mouse or similar mouse from that genus. At first I agreed with you that it might be a rat but using the songbird as a scale item it doesn’t make the rodent look so big anymore.What is that in the #6 picture? A rat? Seems too big to be a field mouse.
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I can’t positively ID that flycatcher as there are just too many similar species, but they are all in that mouse-sized range.