Itheblaze;
It's really not that I feel any need to un-romanticize your stories but I do like to offer the truth to a story, when available.
Monkey ESP.
This story, while again a great story, is based on an exaggeration of the actual data from the study of the Japanese Macaque Monkey (Macaca fuscata) by Japanese primatologists in the late 50's and early 60's. This story comes from a brief reference, to an unfounded (by the data) phenomenon, alleged to have occurred, by Dr. Lyall Watson, in his book Lifetide (1979). This reference was developed, by Ken Keyes who wrote the book The Hundredth Monkey, into a method to bring about social change. The truth that the "phenomenon" did not occur as Watson alleged has been available for many years (Ron Amundson 1985) but is not likely to remove the concept from those with an agenda toward steering social change.
Psychic cats and dogs
A study of ethology, perhaps even a simple cursory look, should dispel the notions attributing other-worldly abilities to animals.
The actions of your Grandmother's cat is a consequence of Observational Learning.
You wake up at a consistent time. The cat gets fed or let out or some other interaction with you at this time. The cat survives on an internal timing mechanism which synchronizes with your normal waking time. When you don't wake at that time, it's internal clock and learned behavior kick in and it interacts with you, even though you are still trying to sleep. Most pet owners can relate to this intrusion. And, yes, the behavior can even coincide with your change on weekends. Animal clocks can cover sequences over extended times as evidenced by their mating habits, nomadic traits, and our 7 day schedules.
I've said it before and I will say it again, Walt Disney was the worst perpetrator of giving animals attributes they simply do not possess.