No, any node can arbitrarily record any transactions it wants without miners.
Mining's primary purpose is to provide security for them.
I can write a transaction down on a piece of paper and leave it on my desk, too. It means absolutely squat until such time that some miner somewhere provides a block that is added to the public ledger known as the blockchain. Mining's primary purpose is to confirm the validity of transactions by adding them to the ledger through proof of work hashing. If my transaction never makes it into that ledger, it may as well never have happened. Expand upon that and see what happens. A whole bunch of blocks created doing nothing but generating block rewards that can never be used because no transactions are ever included in the blocks. Extreme case? Absolutely.
"Empty" blocks are not really empty either: they still include every transaction mined by the prior blocks.
And since 1 block is not sufficient to confirm a transaction, it's really the block 5 down the chain which is beneficial to the transactions in the block mined anyway.
No, empty blocks do not include every transaction mined by the prior blocks, they include a way to get to a parent block. That block might have the transaction, or it might not... but it also includes a way to get to its parent block and so on back to the genesis block.