Did Bengalis, Tamils and Gujeratis see themselves as something different from European traders? Or, to a Gujerati, was a Bengali as foreign as the British or Portugese?

There was no "Indian" identity as such during pre-colonial times, but there was a wider, more subtle identity (reflecting what we might call a common "civilization") that Bengalis, Tamils, and Gujaratis all shared. They worshiped many of the same gods (or at least, regional deities that were associated with a common pantheon of gods), observed many of the same customs and taboos (such as the prohibition of beef), and had broadly similar systems of social organization (based around jati and varna). All of these things would have made a Tamil or Bengali far more recognizable to a Gujarati than an Englishman or a Frenchman.

A good analogy for understanding pre-modern India would be to compare it with pre-modern Europe. Just as pre-modern Europeans had a concept of "Christendom" that included many different European groups who shared certain broad commonalities, pre-modern Indians had a concept of "Hindudom" (not a technical term) that included many different Indian groups who shared certain broad commonalities. The French, Italians, and Spanish may all have vast differences, but they nonetheless have far more in common with each other than with someone from India or China, and they themselves would certainly acknowledge this. Likewise, different Indian groups, despite their vast differences, have far more in common with each other than with aliens from Britain or France.