I recently came across these five questions posed to "Pagans who believe that the Gods are merely psychological archetypes and are created by the mind of [hu]man[s]." I will answer each in turn. (But first, let me say that I object to prefacing the word psychological with the word "merely" -- something I've written about before here.)

1. Do you believe that the Gods can assist you with anything physical in nature? If so how can the Gods assist you with anything physical in Nature given that they are only psychological?

I believe that the gods can manifest as physical symptoms, for the same reason that psychological conditions manifest physically.  I do not believe in magic, causing change at a distance without corresponding physical action.  This applies to us and to the gods.  So if the gods want to move something physically in the world, they will need to use our bodies to do it.

2. Do you believe that the Gods can assist you in areas of the world where human population is sparse?

Yes.  Every person contains within them a pantheon of gods.  We carry this around with us everywhere, even to the proverbial desert island.

3. Can the Gods assist you upon death?

I don't believe in the survival of consciousness after death, so this question doesn't make sense to me.

4. Do your Gods exist after humanity goes extinct?

No.  Although there may be other species that have their own gods -- like whales and apes perhaps. 

5. How does your Gods relate to Nature if they are psychological?

Nature and psyche are the same thing, but seen from different perspectives.  Psyche is nature seen from within.  Nature is psyche seen from without.  So the gods of nature and the gods of the psyche are one and the same.