Android apps are written in Java. iOS apps are written in Swift (previously in objective C). Mobile apps only run on the client device (ex. phone). Most mobile apps call a web API for server-side processing.
To publish an Android app, you need a Google Play Developer Account ($25 USD One Time Fee). To publish an iOS app, you need an Apple Developer Account ($99 USD Per Year). To publish an iOS app using a business name as the publisher, you need to choose the Organizational Apple Developer Program, which will ask for the DUNS number of your legal business entity. The fastest way to get a DUNS number for this purpose is to use Apple's integrated DUNS number lookup/request process. Apple will use the real name of your business (no DBAs accepted) as your app's publisher name.
Mobile API Data Format
Between JSON and XML (typically SOAP/WSDL), choose JSON. It is more concise and easier to read/write/parse.
Mobile API Request/Response Variables
Pay close attention to the variable structure (ex. object vs array) of the JSON request/response. The top-level structure should always be a standardized object because that provides the best clarity and flexibility for top-level variables. Requests and responses to/from the mobile API should have clearly casted variable types (ex. float or string) to prevent unexpected-type errors on both the mobile app and API.
Do not ask for more permissions than you absolutely need. You will assuredly lose users when asking for suspiciously overwhelming permissions (ex. full contact list, start-call power). You can always change the app permission list if you need to add more later.