Learn French: Attends un instant, j'arrive. - Wait a moment, I am coming.

You drop the 's' for the tu command form, but only for regular -er verbs like parler (to speak) which becomes parle. Since attendre (to wait) is an -re verb, it keeps the 's' in the imperative: attends.

Why use j'arrive instead of je viens to say 'I am coming'?

When you want to say 'I am on my way' or 'I will be right there', native speakers use j'arrive (literally 'I am arriving'). The verb venir (to come) is usually used when specifying where you are coming from or who you are coming with, like je viens avec toi (I am coming with you).

Why is it j'arrive in the simple present tense if the English translation says 'I am coming'?

French does not have a direct equivalent to the English '-ing' tense (present continuous). The standard present tense covers both 'I arrive' and 'I am arriving' or 'I am coming'.

Could I say attends un moment instead of un instant?

Yes, attends un moment is perfectly fine and means the exact same thing. Un instant is just another very common way to say 'a moment' or 'a second' in French.