Does the The Ethereum network status monitor (ethstats.net) include blocks with 0 transactions? Thanks in advance.
Yes, blocks with 0 transactions are still valid blocks, and add to the security of the chain. There would be no reason not to show them, given that a block with 0 transactions potentially has other important characteristics, such as uncles.
Note that transactions and uncles are stored separately from one another in the main body of the block, in two different lists. Block explorers, including ethstats.net (and etherscan.io), subsequently report them in two separate columns. Note also that when 0-transaction blocks are reported, they're reported with other useful attributes, such as block difficulty, block time, and network hashrate.