"He has not eaten today."
Translation:Él no ha comido hoy.
yeah, when dealing with third person singular and plural it's not always good to drop the person. in a conversation you can once the person is established, but on dl you might want to keep it. It wont take your hearts for including it. I tend to always include el and ella, but leave off the person when it is ellos or ellas.
It listed both "hay" and "ha" as translations to have. Does hay have multiple meanings? I always learned to it mean "There is/There are"
On its own it does, but there is also the construct "hay que", which indicates that something is necessary or should be done:
Hay que lavar los platos = Someone should (has to) wash the dishes.
Perhaps it has something to do with that.