"He is rarely here."
Translation:Ritkán van itt.
I will take your word for it that "Ritkán van itt" sounds negative, and "Ritkán itt van" sounds positive. I would not know. But the rest of the examples you gave I cannot understand at my point in this course, for they have several words I do not know. But thank you for the first sentence!
I would say Néha itt van instead of Ritkán itt van. Sounds more natural.
I took this one and it was correct, independent of the usability.