Yes, but I don't know how to explain :S
Hayat is the whole life on Earth: other people, animals, earthquakes, economy, cars etc.
Can is more personal: soul, endurance to live, spirit, heart(?). It's the "psychi" in Greek. :D
There are some expressions that sound better with "can" and vice versa:
Can vermek = to die
Canı sıkılmak = to get bored
Canı istemek = to desire
Cansız = lifeless / dead
Canlı = life'd / alive
And so on. Try to learn the expressions one by one as you come by them.
"Hayat" comes from Arabic and refers to life in general. "Can" was originally Persian "Jaan" (which was adopted by Hindi and Urdu as well), and refers to the life-force. That would explain how "canım" can also be translated as "my love"--because the beloved "gives life" to the lover.
It can be your own personal encyclopaedia. :D
The point is, if something is, in your mind, an unchangeable fact, then the "-dir" is justified. We explain it as "encyclopaedical truth" but, it doesn't necessarily have to be a sentence from Wikipedia. If you're telling a faerie tale to a 5-year-old kid, and say: "There are tooth faeries that come at night," then go ahead and use "-dir". It doesn't have to be true; if you treat it as a truth in your context, then the "-dir" is justified.
English speakers are having quite difficulty in understanding the difference between can and hayat. Can is quite personal/physical/related to soul. While Hayat is life, as in English. In my native language we have jaan,zindagi and hayat all meaning life but used in different ways. Also we have many words for Love unlike in english like mohabbat, pyar, eshq, unsiyat, chahat, even hubb but every word is used quite differently. In English you would love your parents, siblings, wife, girlfriend etc. But in my language use cannot use eshq for your parents , it can be use only for romantic love or love of god (Ishq-e- ilahi) for them you gotta use mohabbat or pyar. Similarly in turkish you can not use aşk for your parents, it can be used for romantic sense or love for god. Cultural differences.
A CAT has nine lives, the cat is the subject.
you have nine lives, Sen in dokuz can ın var.
I have nine lives, ben im dokuz can ım var.
he has nine lives, o nun dokuz can ı var.
you have a cat, sen in kedi n* var.
I have a cat, ben im kedi m var.
he has a cat, o nun kedi si var.
you can also omit "benim, senin, onun, bizim, sizin, onların"