Can I wash the outside of my engine while it's running

Yes, you can and fortunately your car model has steel exhaust manifolds instead of the the more brittle and temperature shock sensitive cast iron exhaust manifolds.

If you had those (cast iron type) you'd have to take care not to hit an extremely hot manifold with the much colder water from your hose/sprayer nozzle, as the big temperature differential shock unevenly placed on the hot manifold could cause a crack.

In any case, when washing a running engine it's always best to do it starting with an engine that's relatively freshly started and not one that's very hot from a previous longer running time to minimize any temperature differential shock to a certain few components when you first begin spraying.

Tho keep in mind that the vast majority of your engine and its components will never become hot enough for this temperature shock to even be an issue.

It's important, as oldturkey03 already stated, to stay away from the intake and avoid soaking the electronics!

Keep 'er clean! 😁