There is no general answer, I'll answer for the specific cases:
Research Experience (singular)
Publications (plural), or "List of Publications"
Education (singular). A better term is "Academic Record" IMO.
Honors and Awards (plural)
In points 2 and 4, going for plural makes sense because there is more than one publication and more than one award involved. In pt. 3 there may be more than 1 institution involved, but it doesn't say "institutions", it says "education", which means sum total of everything you obtained by going in these institutions. In point no. 1 also, the phrase "research experience" talks about all the research you have done in your academic career. "Experiences" would refer to the experiences you had during the course of your research. That's not what they are asking for!
Hope that helps :)