Are the first three shots the same bird? Those shots look like a female Cassin's Finch to me, with that raised crest in the first shot. The male bird is a House Finch. Where were these shots taken?
The first two are one bird, the third is a different one. On the feeder at the same time. They were taken in Maine. So doesn't seem like they would be Cassin, but they seem more heavily striped than a typical house finch female? The crest was VERY pronounced - never seen a non-crested bird have it raised that much while, and while just sitting and chilling.
House Finches have brown streaking on the flanks, whereas Purple Finches don't really have the brown streaking, and instead have smudgy red streaks on the flanks. That's the easiest way to tell, at least! Here's a comparison shot, with the House Finch in the foreground (not my photo):