This is illegal. The government, for the most part, doesn't actually care whether your income is in legal tender, bitcoins, foreign currency, gold, stocks, pork belly futures, or whatever. All individuals and corporations are required to pay tax on the market value of whatever it is they receive as income. If you're attempting something like this and don't understand the tax implications, you should ask your accountant or tax advisor about taxation of barter transactions for information specific to your situation.

They had to declare it anyway, for the above reason. And if/when they do exchange their bitcoin for legal tender (or anything else for that matter), they also have to declare any increase in value of their coins between when they mined them and when they sold them (if, on the other hand, their coins decreased in value during that time, they can declare the loss and in some cases get a tax refund for it). Again, ask your accountant or tax advisor about capital gains and losses for more information.

Every block is guaranteed to have at least one transaction: the transaction that pays the miner his newly generated bitcoins! There is absolutely no problem with this transaction being the only transaction in the block. Note also that trading bitcoins for fiat money also involves transactions just as spending them does.