Help updating a shop. I never done one before

Hi I wonder if you lot can help me. I have been asked by a friend to do some updates to their website but I've never used Zencart before so I need help. I'm sorry if I ask a lot of questions I just do not want to mess it up.

Website: https://www.ecloudonline.co.uk
Zencart: 1.5.1
Database: 1.5.1

Here are a few of the things they want.
1, At the moment when you go to the domain it takes you to a loading page. They want it to go straight to the shop.
2, They want the Navigation that goes just under the logo they want reordering (Home, Store Locations, Accessories, Atomisers, Batteries, eCloud Premium Liquid, Starter Kits, Contact Us)
3, They wants to update the store locations as some need adding and some need removing.

First of all, to prevent "messing it up" the new site should be built in a separate location from the existing. Whether that is on a local computer or a separate directory on the host is somewhat up to you and the resources available.

Second, check out at least the following instruction for upgrading: http://www.zen-cart.com/entry.php?3-How-do-I-rebuild-my-site-on-the-new-version-instead-of-upgrading

Third, upgrading to 1.5.3 then should also look at/follow the tips/changes of the following thread: http://www.zen-cart.com/showthread.php?214916-Important-announcement-about-POODLE-and-payment-security
and then should subscribe to the parent thread: http://www.zen-cart.com/forumdisplay.php?2-Zen-Cart-Release-Announcements

And should also apply the known patches for 1.5.3 at: http://www.zen-cart.com/showthread.php?213868-Known-Bugs-%28and-fixes%29-with-v1-5-3

As for the other things: I haven't looked at the website to fully understand 2 and 3, but 1: simply install ZC so that it is in the root of the uri used to get to the site. If that means to install it in public_html so be it, if you have control of where the uri points, then can install in a sub-directory off of public_html and then have the uri point to the sub-directory. That would be my recommendation which would also make future updates easy to perform.

First off though, want to get the basic install up and going and then can work on those customizations that are desired.