Is it possible to install App in iPhone directly without iTunes or Appstore?
It's been possible to install (or 'sideload') apps onto iOS devices without a jailbreak or iTunes (though iTunes may need to be installed) for a year or two now. There's a few applications (e.g. Saurik's Impactor, CopyTrans, Appandora) around to do this, and one can also use Xcode (see here). 

This is something that will be of inccreasing interest now since Apple has recently removed the app store from iTunes 12.7, although it seems that Apple says it will still be possible to use iTunes to transfer apps.