I would search the Tutorials/FAQs and Wiki and the forums on:
Zones

Zones are designed to "filter" what addresses are able to use various Payment, Shipping and Order Total modules ...

As to why things are not showing in the Catalog that you see in the Admin ... good question ...

If you don't know about Zones, then it sounds like you do not have any Zone filters set yet ...

Do all the shipping modules have the green dot or the yellow dot?

NOTE: if they have the red dot, they are not installed ...

Also check that each one has the Enable set to true ...

I am not quite sure where the reference to currencies fits in here on shipping ... but you might make a separate post on questions about currencies ...

What version Zen Cart are you running?

Clean Install or an Upgrade? If an Upgrade, what did you Upgrade from?

Can you check that both of the configure.php files, on the server, are using the same database:
/includes/configure.php
/admin/includes/configure.php