The vent comes off the top of the trap arm. This is what breaks the siphon.
If the vent comes off lower then the trap, it will siphon.
One of those is shaped like an S, that is a "No go". Can't do that.
You need at least three vents there.
The tub, the lav and the washer. These need vents.
If the lav were closer, you could wet vent the lav and the toilet together. So really, you're looking at four vents there.
When you pull the permit and the inspector comes out, he can verify the job.
There was a while there, where I was getting a plumbing inspection every day. I ran a three man crew and we plumbed five "3-bath" homes a week. Those were splits with a lower floor groundwork. You can't do them that fast if you have a crawl on the first floor.