Hi,
I could install ZCash and although I read the FAQ, this is my first true experience with electronic currencies. I still have several questions. Thank you for your indulgence.

1 block solved = 1 ZEC ?

Does “hitting a block” mean doing the last step of resolving a difficult mathematical problem, partly solved by other nodes in the computing network? (The node doing the last step of solving a block being the only one rewarded?)

Is “hitting a block” like a lottery ?
(The most you are “playing” the most statistical chances to win one day, but no guarantee at all ; some nodes going to be “happy” ones and others “unhappy” ones?) 
Does the “slow start” of Zcash during the 34 first days mean that the Zcash Team can adjust the number of ZECs to mine to keep the statistical chances of winning one more or less the same during this period, as the number of ZEC will ramp up, but the overall computing power too?

To whom is a “reward” allocated? To the rpcnode who solved the block? To a t/z address created on that node ?
Thanks.