First one: I was very young when this happened, about 4 or 5, and this happened in the early-mid 2000s. I have a distinct memory of a freakishly large moth flying into my home in Edison, NJ, and my parents’ attempts to evict it. I only saw it from a distance, being too scared to come closer, but I remember it being a dark coffee-brown color and had a triangular shape (not unlike some tiger moths).
The second one is much more recent and it happened around 2015. This was at my grandmother’s house in India, which doesn’t really have as well-known an insect fauna as the US, so I’m fine with just a general ID. This one was a bright green insect (looking something like this planthopper) about the size of an average butterfly, with large wings held to its sides. It entered the house at night when the balcony doors were briefly opened. I approached it assuming it to be a leaf, and it suddenly started to fly around the place before we let it escape. I’m not sure if this one was a butterfly, a moth, a weird katydid, or a giant planthopper.