When Stack Miners commit bitcoin - does all the bitcoin get distributed to the stackers stacking or does the system take a percentage of the bitcoin for itself? And if so what is the percentage?
It goes to Stackers who have clinched at least one reward cycle slot. Also, all BTC sent to unused slots (and prepare-phase slots) gets burned. Bitcoin miners only get a Bitcoin tx fee. See SIP-007 for details.
So the foundation of the stack gets or takes no percentage of bitcoin committed by the miners?
Correct. All BTC goes to Stackers if it isn’t burned.