Does a small concrete slab need control joints?
No. My rule of thumb (can't recall where my thumb got it from) is 12 feet/4meters before you really need a control joint.
Reinforcement is always a good idea.
This document has a great deal of vague handwaving, and on page 11 gets to a specific recommendation from the ACI of &quot;24-36 times slab thickness&quot; which in your case is 7-10.5 feet. that suggests that 0 or 1 control joint might be the right number (with the 1 making two 4 foot squares per another recommendation found in the same section of the document that the slab segments defined by joints be square or near square.)