Remember also part of senility, as young people see it, is not knowing something. According to some studies I have read about the fact is older (possibly senile) people can process information as accurately as younger people just slower. They can solve puzzles, use logic it is just a slower process.
Alzheimer's is something you don't want to get into since it is a much more complex issue than it appears. A lot of the side affects are seen as old age but are actual just human responses to the situation. Irritablity, burst of anger come from the frustration and inability to do something you know you can do as it is from physical loss of emotional control.
If you want info on Alzheimer's I know some and have experience as well. Most of it from the layman's point of veiw.
Also senility is a pretty broad term it could mean several things to me. but here are a few ideas.
Person can't take 10 for anything. You know longer operate at a standard. You can assume they still can perform some task without risking major failure but it is possible to fail even at the most mundane task.
Failure sometimes triggers extreme emotional responses. Maybe a will save when they fail at something that should have been a success or lose it. Losing it as defined by the person; be it rage, crying, sobbing, giggle fit etc.
It is such a role playing guided thing that it is hard to present cold hard rules for it. I mean you can certainly decrease stats and such but that doesn't reflect the true affects anymore than they do for stats for a child. I think this is more the area of role playing notes than mechanics.
later