You mentioned Proof of Work. Can I mine IOTA’s?

You should not compare IOTA Proof of Work, with the Proof of Work mechanism that is commonly used by Blockchains (e.g. Bitcoin). IOTA's Proof of Work is directly comparable to Hashcash, as it serves a similar purpose to prevent spam, and in our case, also to prevent sybil-attacks. Because of the way consensus is achieved, there is no way to earn IOTA's through the computational effort required for making a transaction. As such, there is no "mining". One can argue that you're being directly rewarded by having no fees on your transaction.