Hi Amara,
Almost correct...
Fiori is a design paradigm - not a methodology.
Agile is a methodology that we generally recommend for UX projects... so that the designers, developers, testers, and everyone else work fast and communicate efficiently to get the job done.
And if you need features such as offline or native then your choice is either HCPms (Cloud) or SMP (On-Premise)... these will let you extend a Fiori app to include the offline or native features. Or you can write a completely separate offline or native app as well.
I'm not an expert on SMP so can't answer your last question, but I would suspect that the answer is no. ITS is now a very very old technology and depending on how your app was written is likely to have used a stateful transaction process. Fiori and other modern user interfaces use a stateless process. This makes more efficient use of resources and reduces risks such as reduced likelihood of data loss.
I wouldn't consider it appropriate to mix ITS technology in the same app as Fiori or any native or offline app as the paradigms are too different. However you can provide a link to an existing ITS app by it's URL.
Rgds,
Jocelyn