Fruits and berries are not vegetables. But potato man is :)

This is not true. E.g. zucchinis/courgettes are fruits but are widely considered vegetables: https://en.wikipedia.org/wiki/Zucchini

Same for eggplants/aubergines: https://en.wikipedia.org/wiki/Eggplant

That is correct. "Vegetable" is not a category which would be useful to a biologist.

Tomato is a berry.