yes those are all valid ways of staying anonymous - you can also use tumbling services which take your coins, mix them up, and give you back different coins to a different wallet minus a small fee to anonymize coins bought with your credit card etc you could also buy another coin with btc, then trade it back for btc to a new wallet to get fresh coins (i.e. buy monero with btc, then btc with monero, deposit to new wallet -fresh coins)
ATMs and private buys off localbtc charge very high rates, usually 9% lowest up to 15% or more
if you registered to the mining pool with your own information (email/name) and used your own IP they could likely track the coins to you that way if they really cared. but no one really cares that much. there are companies who's whole business is analyzing the block chain though
monero is better for anonymity. monero automatically tumbles/mixes coins and you can keep your transaction history private, so no one can know the sender, receiver, or exact amount of a transaction.