Moore's law is about the number of transistors on a processor. Processor speed is generally a byproduct, but hasn't kept up in percentage terms for quite a while now.
That's mainly because most software written for general purpose CPUs doesn't scale well to many threads. Mining does scale well, so I'd expect hash power to increase with the number of transistors.
Minnig will always remain profitable for "enough" people. ALWAYS.
That remains true until all Bitcoins are created. Then the only reward is transaction fees which as of right now is pretty much nothing.
Total transaction fees will surely increase over time. Either by the number of transactions increasing, or the fee per transaction, or both. At the moment mining is effectively paid for by inflation. As that ends, we may find that Bitcoin transactions are no cheaper than credit card ones.