"I am not hungry at all."
Why is this not in the past tense, like it is in the positive おなかがすきました？What would おなかがぜんぜんすきませんでした mean in English?
Well you can figure that out by knowing the literal meaning of the phrase: おなかがすきました means 'My stomach became empty' (so that's why I am hungry right now), so when you say ぜんぜんおなかがすきません you express the current state of your stomach: 'My stomach is not empty at all' -> I'm not hungry right now. おなかがぜんぜんすきませんでした probably refers to not being hungry sometime in the past.
These look fine. ぜんぜん（全然 ）can go in either place. As japan_ichiban explained, お腹がすきません is "I am not hungry," and お腹がすきました is "I am hungry." Or with all kanji, some arrangement of 全然お腹が空きません. It is useful to notice that the すき here (空き), is not the すき(好き) we learned earlier in the course.