The usual deal is that there are a couple of "shops" to be performed that have high purchase reimbursement and/or fees ($100 or $200 fee is not unusual in the scams). You now have "earned" a couple hundred bucks of the scam money sent, maybe reimbursed yourself for some items and now there is $1800 or more left that your 'last shop' is to send by Western Union somewhere. Of course they don't care what size the check was--it was fake. And they don't care how much you spend--your loss. And they want the fee to be attractive enough you fall for it. All they really want you to do is wire transfer $1800 to them, and when the check bounces, you have sent them $1800 of YOUR money that is not recoverable.
To your specific questions. If you look at checks you have written on your account that have been cashed you will usually find the account number--either written by the recipient or added to the check by the bank. That is not an issue in the faked check scams as the checks are forged and will not be returned to the forger anyway.
Some merchants and e-vendors do have the ability to receive payment with only an account number and routing number. I pay most of my monthly bills by providing them with this information. They do ask that I confirm the payment authorization usually by clicking on a pop up. I feel certain that someone with evil intent could probably do this as well without my ever knowing it was happening until it was done based on a check I wrote or a check I cashed. There would be interesting discussions with my bank because there are safeguards and limitations to who is authorized to do such things so it would be relatively easy to track back to them.
The game with these scammers is that Western Union payments can be picked up with little or no identification at any of many locations. In my area I could purchase a faked but authentic looking drivers' license for $60 at the flea market, so if Western Union wanted ID to pick up the money, I could provide the name on my faked license and then disappear without question.