One that I wish we asked the subjects in our studies is: When do you normally go to sleep each evening and when do you normally wake up? This can get more detailed, but these 2 basic questions can allow segregation into morning or evening types (or both).
Deep phenotyping is critical to a better understanding of the genetic influence on disease risk phenotypes, and so one should collect lifestyle data - like diet, sleep, exercise - which all influence the genotype-phenotype association (these are called gene-environment interactions). If you can come up with phenotypes that distinguish different paths to the "same" disease outcome, that would be relevant to ask. In other words, there are often many paths to a very similar disease outcome, but as those paths are different, the disease may be slightly different. This requires sub-classification of disease - think of the different types of breast cancer. So, collecting these phenotypes, if you know them, in conjunction with diet, exercise, etc, will give you some very interesting possibilities.