In this paper you will find examples that fits with your first question:
http://www.sciencedirect.com/science/article/pii/S0040938303000053
"Elliptic rational spaces whose cohomologies and homotopies are isomorphic"
Tetsu Nishimotoa, Hiroo Shiga, Toshihiro Yamaguchi.

The authors consider a family of elliptic spaces that are not formal nor coformal.