I tried to download old family photos from my brother's account. They say you could download photos that was uploaded in a certain time interval, "from dd. Mm. Yyyy to dd. Mm. Yyyy". Well, it told me that it couldn't download those, instead it downloaded the latest photo and counted as one for today. What the heck?
They say you could download the photos in the original uploaded size. Hardly. The biggest image was 1080x1080, since at a standard width of 1080 pixels, Instagram keeps your photo its original size, as long as its height is between 566 and 1350 pixels. If your photo is less than 320 pixels wide, it'll be stretched. If it's more than 1080 pixels wide, it'll be shrunk down. So no, you won't get bigger than that.
I will update this review as soon as I could.