Same here. I have removed all of the updates, so now I have the original, pre-installed version on it. This does not start automatically, and since I don't use it, I never update it.
But in general regarding running applications: you should ignore them. The android os is designed in a way to keep many applications in the cache, so when you need it, it loads pretty fast. If you dont need it, it remains in the ram, but basically frozen. If the ram is getting full, the last used stuff will be removed by the os to free up space.
Thats why the tons of ram-cleaners are completely silly. Who cares if the ram is 80% full. The os will do the job if you need space.
For sure, badly designed apps might cause problems if they are really running in the background, and using more than minor cpu power. These should be killed, and removed.
I dont think google music player belongs to such, but I simply removed, as I never need it.
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