Desperate need of help!

okay
I have 2 concerns 1st I have noticed water leaking on the driveway after checking when washer and diaswasher draining it leaks between outside bricks and foundation.So I called a plumber he says he has no idea but he did say my drain needs a trap to prevent sewer gas , I'm not sure where to start
here a picture. the previous owner sawed the vent pipe off and run washer machine hose into it. sorry picture is in attachment

any ideas on trap would be appreciated they left this plumbing a mess
also suggestions on drain leak?

Thanks

A P trap is absolutely required on every fixture's drain. The toilet has one built into the base, but all the rest must be installed. I'm sure you have traps under your sinks. Take a peek and you'll see it. Traps simply create a water seal to prevent sewer gas from entering the house. My advice to you is to have your plumber survey you home and install traps as needed.

Find a better plumber. The one who's baffled by the leak is a pretender.

That looks like a job for a licensed plumber. you need a trap and a vent for it.

drain

1. Find a real plumber.
2. Let him diagnose the leak and find a cure.
3. Have him install a correct washing machine connection.
4. The have him reconnect the piping properly.