Why does Violet Evergarden seem to have a habit of biting things?
She has trouble writing with a pen and in the second episode we see her adjusting her fingers to type better. This means that her prosthetics are not perfect.

I disagree with point 1, it's much more likely that it refers to her following Gilbert around and obeying him like a loyal dog rather than anything biting related.

For point 2 it is very likely the feeling related reason.