Blinkmoth Nexus can be the target of its last ability after activating its middle ability. Activating it after it has blocked a creature won't remove it from combat or stop it from dealing and being dealt combat damage.

A noncreature permanent that turns into a creature can attack, and its abilities can be activated, only if its controller has continuously controlled that permanent since the beginning of their most recent turn. It doesn't matter how long the permanent has been a creature.