Can I culture yeast in dough without the dough going sour?
I mean instead of adding new yeast everytime can I take a bit of raised flour and keep it for the next time?
In this situation will the flour go sour? Will new organisms grow in the flour?
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You can certainly maintain a culture this way, though not all cultures will necessarily thrive. Commercial yeast, for instance, doesn't tend to do well with feedings. It basically rises and it's done. Wild yeasts will do much better by being fed.
The degree of sourness in the cultured flour will depend on the specific strains of yeast and bacteria growing in it. You can control this to a degree by adjusting the hydration level and temperature to encourage specific strains of microorganisms to grow.
Here is a link describing how to control some of the cultures in your starter.