[2022] Unable to unlock player avatar icons

Can you describe which ones you are referring to? Past icons such as year-marked icons are typically granted at the start of an event for free (not from a Loot Box) and are not granted again in later years.

Unfortunately no. The Spray, Player Icon, and Epic Skin from each seasonal event weekly challenge do not appear in Loot Boxes. There is no way to get them once that weekly challenge passes.