iPhone iCloud question So when I got a new phone my apps that were downloaded previously still show that they have been downloaded on my previous phone? It's like the little cloud istead of the open.  Is that normal?
Yes, it is perfectly normal. It signifies that the apple account that you are currently using has previously "purchased" the app. Note that you may not have actually purchased the app, in the case of so called "free" apps.

The link what does the cloud icon mean in the app store provides some links to Download your past purchases and iCloud.