"This old house gives me the heebie-jeebies". It means the (haunted?) house gives you a feeling of nervousness, fear and jumpiness.

no, it means you are freaked out, such as "he gives me the creeps"

This comes from the common expression "I get the heebie jeebies". It means I become frightened. Example "When he says his heroes are serial killers I get the heebie jeebies". Heebie jeebies could be translated as "feeling of fear" so it is a noun.

Bianca and Peachey are correct. In answer to the second part of your question, I would consider it a noun.