There are must be a lot of apps that are designed to communicate with server. My question is only about App installed on iOS device + Server side service interaction. Web app is
Are you sure you want to spend time & money to develop your own Server & develop your own API? There are lots of mBaaS (mobile Backend as a Service) providers today such QuickBlox, Parse,StackMob, which are ready to use and they have great Custom Objects API and some of predefined modules. They have great free plans with big quota. Some of them such QuickBlox has Enterprise plan - so you can buy license and they server team update server for you purpose.
So, i recommend not develop your server and think about mBaaS market.
Just about your issue - I can recommend look at QuickBlox Custom Objects code sample and also Custom Objects API. Custom Objects module provides flexibility to define any data structure(schema) you need. Schema is defined in Administration Panel. The schema is called Class and contains field names and their type. I think it's what you need.
Well that depends on what you know, there is reason to choice one of the other
This would reflect on your first question, you pick the language on you needs. Thus if python makes it easier then pick that one.
Again not one that is easy to answer, since it all has to do with requirements. But any SQL server will do. Cassandra is meant for "scalability and high availability without compromising performance" accourding to there website. Do you think you webservice will get many request then it might be a choice to consider.
This again is only going to be answered when you pick the a SQL server and server language.
Start with something simpler, you are really going out on a limb here.
Propably there is some, but you should really start small and work from there.
Twitter started out as a Rub on Rails app and is working on scalability and availability which ruby is not really good ar (that is my person opinion). or Look at facebook they have written a php to c compiler to make php run faster.
The only thing I can say to start code, when you app does take off then tackle the some of the performance issues.
And since you state that you are new to programming do not bite of more then you can chew.
This is a huge question and I don't think there is a best answer. It most depends on what you care about, such as how quickly the development process, how easily the implementation, etc.
And which one is popular, which one is cool, I don't think it make really sense.
In my personal opinion, I'm good at ASP.NET and I can get Windows server easily, so I'll start with an ASP.NET service to provides data.
And, to be continued.