Does it require miners some extra effort to include fee-less transactions in the generated block, provided there is enough room in it?
No, a transaction with or without fee does not change the difficulty. By default settings however there is only 50KByte reserved in a block for transactions without fees or with fees so low they might as well be none. Thats 1000 satoshi currently AFAIK.
Thats typically the coinbase transaction creating new coins, yes. I think these blocks are empty because the miner that mined them did not know of any other transactions at the time or at least not enough. Once a new block is published to another miner they have to start from scratch. In order to waste as little time as possible they would start calculating hashes on a block with no transaction but the coinbase. If the block is found early no transactions have been added yet.