Yes you can send all the data to one profile.
In terms of a consistent datalayer, this might be an issue. Because website and apps are different in the way they trigger data, on an app you may find you are limited as to what data is available or you may find you have more data available, same goes for websites.
It is going to take a lot of planning, normally start with a template where you can tell your developers to fire links and views at certain points on the website and app, This should help keep everything together.
Or you can also use eventstream to stream data into your analtyics and create your own events using the filters.
There are many possiibilities, it is whatever is best for you..