How to check Bitcoind is mining?
Answers to your respective questions:


Since 0.12, bitcoind supports cookie file authentication. This means that on startup of bitcoind, a file with a random key in it is created. Anyone who can present the contents of that file to the running bitcoind is allowed access. Since bitcoin-cli runs locally and as the same user, it can read this file and do so.
Bitcoin does not have any concept of accounts (at least not at the protocol level). Generated funds by bitcoind's built-in miner are sent to an address taken from your local wallet. If you want to modify that, use mining software instead of the built-in miner (which is only there for testing purposes).
The built-in miner is off by default. You can enable it by setting gen=1 in the bitcoin.conf file, but I would strongly discourage you from doing so. The chance of finding a block using that setup is about 1 in a billion, if you leave it running for 10000 years. If you insist on using your CPU for mining (which won't ever be profitable), at least use optimized software like bfgminer, and sign up with a pool, so you can get small rewards for work, rather than waiting for a lottery you'll never win.


Update august 2016: The internal miner is removed entirely in Bitcoin Core 0.13.