Q. A few questions concerning elderly patients. A patient that has lost most of his memory but is still rational and understands and can follow a conversation, is that patient considered a shote and is he exempt of mitzvos or can he still make kidush and havdala for someone else?

A. The Talmud (Chagigah 3b-4a)i lists three actions that are characteristic of the disorder: (1) going out unaccompanied at night, (2) sleeping in a cemetery and (3) tearing one’s garments.  On 4a the Talmud provides a fourth illustration: (4) a shoiteh loses everything that is given to him.  Rashi (ibid.) explains that a shoiteh is exempt from Halachic obligations, exonerated from punishment, and prevented from participating in business transactions.
Rambam (H. Edus 9: 9,) rules that the term shoiteh is not exclusive to one who walks naked, destroys objects, or throws stones. It includes anyone whose mind is confused and whose processes of thought or conduct are adversely affected, even if he is able to communicate and respond properly.
The S’mah (C. M. 35: 10) contends that shotim are granted special treatment in Halacha because they are detached from reality. They suffer from cognitive deficiencies, and consequently, lack a typical awareness about the world around them. 
Some Poskim however maintain that the characteristics mentioned in the Talmud are essential to declare someone a shoiteh (Beis Yosef E. H. 121 quoting Maharik, Zichron Yosef E. H. 10, Tzemach Tzedek E.H. 153, Divrei Chaim E. H. 1: 53 and 73 – 85, et. al.)
Igrois Moshe (E.H. 120) rules that the status of shoiteh only applies to the sufferer for the time during which they are in their confused state and only regarding matters in which they are confused. (See also Torah Umaddah 12: 158-178) in regards to the Halacha status of patients who suffer from Alzheimer’s disease.)
Horav Shlomo Miller’s Shlit”a opinion is that even according to the view of the Rambam, serious memory loss per se, does not qualify someone as a shoiteh, unless he becomes detached from reality and recites kidush on weekdays. But if he knows that it is Shabbos and is able to recite kidush he can do so also for someone else.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit”a