Does molarity change if you decrease volume? For example if the solute of the solution contains $\pu{0.5 mol}$ and the total volume is $\pu{0.5 L}$, the molarity would be $\pu{1M}$. But if I take a portion of that solution, let's say $\pu{0.1 L}$, would that molarity be still $\pu{1M}$? If it were that way, the solute would be $\pu{0.1 mol}$ too. 

Or, do the moles of the solute stay the same $\pu{0.5 moles}$ and the molarity would change to $\pu{5M}$? 

So my question is, does the solute decrease when the volume decreases too?
No, solute will not decrease if volume will decrease.But molarity will increase for sure, cause molarity is the amount of solute in litre of solution.

Consider container A in which you took 1 litre of water and added two spatulas of NaCl and in another container B you took 0.5 litre of water and added two spatulas of NaCl. Now which container has greater amount of solute , the second one that is container B ,hence molarity of container B solution will be greater than container A.

Hope it will work to clear concept.