When I bought recently, I wasn't asked the source of my downpayment as long as I could show I had the funds going back at least 3 months. I presume they do some sense check against income sources (i.e. if you have $300k down payment, but only make $30k/yr and you're 25, they'll ask where it came from), but otherwise if it was "seasoned" (you could show you had such funds over some time period), they didn't dig further.

Now that's much more scrutiny than lenders were showing back in 2007. Back then, if you had cash in a bank account, all good.

In terms of laundering, it's basically passing money through enough legitimate transactions as to conceal the source. So let's say you have $1M in money from illegal activities. If you can get it into a foreign bank account, you could transfer it to the US, buy a house, sell 2 years later. If anyone asked where the money came from you've got a few years history of legitimate investments.