Do stars have any kind of cycle?

Yes most stars do.

Our sun has a 22 year cycle, every 11 years it swaps magnetic poles and gets covered in sunspots.

Also it spins every ten days.

Well, there are Cepheid Variables, stars that get brighter, then dim over a particular period. There are unstable giants, which can brighten and then dim at irregular intervals. Our sun goes through a 22-year less active/more active phase, where sunspot activity and flares decrease, then increase again - and it's thought this pattern to have been discovered in some nearby stars as well.

All stars undergo evolution, gradual change over their lifetime. Many stars are variable in brightness in a cyclical way. Usually this is caused either by their being double stars which pass in front of one another (eclipsing binaries) or stars which vary in size, colour, and brightness (pulsating variables). An example of the former is Algol (Beta Persei) and an example of the latter is Mira (Omicron Ceti).

Stars DO DIE , science shows you that , just read about it ,

And btw , most of the stars you see are already dead you can only see the light they emitted while still ''alive''

Yes its called the star cycle.