What does "ease" mean in the phrase "dharma gate of ease and joy"? What is the "ease" of the "dharma gate of ease and joy"? Can an unelightened person achieve it outside seated meditation?

Ought I imagine everything is difficult, or everything is easy? How can we be effortful in our everyday lay tasks?
Dogen means that when you practise zazen you let go of troublesome thoughts. When you do this your state is one of ease (in the sense of 'being eased' rather than 'easy').

I think Dogen would have agreed with Hui Neng on the subject of enlightened and unenlightened people : One foolish notion is enough to shut off Prajna, while one wise thought will bring it forth again.

When not doing zazen, we should still be practising awareness (some sanghas refer to work in the temple as 'working meditation'). Although sometimes we need to think about difficult stuff. Zazen is just a time when we don't have to and can let go of everything.