Comment: I forgot to answer this part.. sorry..

"can something be fully one thing, while being fully another thing completely different at the same time?"

A blue square can be fully blue and fully square at the same time, while blue and square are completely different concepts.

The only time logic is in question is if the concepts are mutually exclusive.. like with a square circle. Since Jesus is an example of someone who is fully God and fully man, there is no mutual exclusivity with the concepts.. They are different categories, like blue and square, or person and substance.