Updated: Oct 30, 2017
No, Anoncoin is not directly related to the Anonymous collective. Anoncoin can be used by anyone who values privacy and anonymity, including those associated with “Anonymous”. Some people involved with Anoncoin might be involved with Anonymous, but even if this were the case, this is irrelevant. The original Anoncoin logo of the headless businessman that is usually associated with the Anonymous collective has since been changed in order to distinguish the two entities.
The current block reward is 1.25 ANC. This is expected to halve to 0.75 ANC around August 2018.
There are many coins and services that provide increased privacy (using such things as CoinJoin, SharedCoin, DarkSend, other coin mixing services and ring signatures), however, you should not confuse privacy with anonymity.
You can download and install it from I2P website.
See this list of exchanges.
See the mining pools listed here.