Learn French: Il demande pourquoi le délai est très long.

Because this is an indirect question (reported speech). While a direct question might use inversion (like Pourquoi le délai est-il si long ?) or est-ce que, indirect questions always use standard statement word order: question word + subject + verb. So it is simply pourquoi le délai est.

Why isn't the verb est changed to the imperfect tense (était)?

The introductory verb, demande (asks), is in the present tense. In French reported speech, you only shift the tense of the second verb backward (like changing the present to the imperfect) if the introductory verb is in a past tense (like a demandé). Since he is asking right now, est stays in the present.

Does délai mean the exact same thing as the English word delay?

Not exactly, it is a bit of a false friend. While it can translate to delay in some contexts, un délai usually means a timeframe, wait time, or deadline. If you want to talk about being late (like a delayed train), you would use un retard. Here, he is asking why the wait time is so long.

If I wanted to say He asks us why..., where would the word for us go?

You would place the indirect object pronoun right before the verb demande. For example: Il nous demande pourquoi... (He asks us why...) or Il lui demande pourquoi... (He asks him/her why...).