At the point of writing this the supply of ether is still "infinite". Every 15 seconds two new Ether are generated.
Currently we are at 107,682,753.47 Ether.
These are from:
Genesis (60M Crowdsale 12M Other): 72,009,990.50 Ether
Mining Block Rewards: 33,168,789.59 Ether
Mining Uncle Rewards: 2,503,973.38 Ether
The change to PoS got delayed a few times ...
Provided you are using the same algorithm that ETH uses for your private chain, you will always have to mine in order to create blocks and process transactions.
Since it is a private blockchain, there should not be many miners on the network, and thus the hashing power should be low. Because of this, you are able to mine with a simple CPU and very little ...
It does mean that an entity has found a way to mine as much, (or more) 0xbtc than some particular mining pools, however, it doesn't have to mean that the public address belongs to a particular individual, it could also be an unidentified mining pool of people which operates like the other already identified mining pools.
In regards to the mining process, ...