1. I added your domain to a number of tools and from the looks of it, you're on shared hosting. This is not an ideal hosting plan, the server that your domain is served from has over 200 other websites.
Therefore, I would recommend possibly changing host provider and also consider purchasing a VPS or Dedicated server.
You could also speak to the guys over at ZippyKid - http://www.zippykid.com/
2. Do you mean once you have installed your customers child theme on there on domain ?
3. Most developers use software such as MAMP (for Mac) XAMPP ( for Mac/PC) and WAMPP (PC Windows server), these programs/applications basically turn your Desktop/Laptop into a local server.
MAMP - http://www.mamp.info/en/index.html
WAMP - http://www.wampserver.com/en/
XAMPP - http://www.apachefri...g/en/xampp.html
Once you have created your local website, you can move it to a live server following the instructions here.
You can also export your Template, Primary, Special Meta settings and Layout Configuration by going to PageLines > Account. Once you have done this, go to the accounts page on your live site and then import the backup file.
4. You could use the Quick Slider which has arrow head navigation.