That is all useful and interesting to me in itself, i've found that much of studying history is about learning what we have no information about!
Do we have any idea of the dynamic between the authorities in Hinduism in this period and Buddhists?
At this period the authorities were mostly Buddhist- this was the time period when the Mauryas were dominant and Ashoka made Buddhism the official religion.
This, of course, probably didn't really affect people on the ground- your average villager would still be going to his village shrine as he always has done. Buddhist monks would have been patronized by the wealthy and so forth.
This was the start of Buddhism's decline in India, however, and by the 1st century CE it'd mostly vanished- and interesting sidenote of history is that some of the original converts to Christianity inthe Southn Indian region of Kerala (which was one of the last areas where Buddhism lingered) may have been drawn from the dwindling number of Buddhists as even today their descendants (like me) still use some Buddhist terms in their Christian liturgy (e.g. Church Councils are called Sangha, just like Buddhist theological councils).
This is the trouble with asking generalised questions about India- the situation really varied from place to place. Western sources tend to draw on information from Bengal and the Indo-Gangetic valley simply because those were the areas with the strongest British presence. British civil servants tended to ask the local Brahmins for information and thus the four step caste system familiar to Westerners reflected a purely North-Central Indian reality filtered through a Brahminical perspective. Unfortunately British administrators then used this information as the basis for many of their policies throughout India as a whole thus resulting in the situation we have today where this notional caste system has been imposed in places where it was never a reality- e.g. in Tamil Nadu there were hardly any caste groups recognised as Brahmins and those that were often tended to be cooks rather than priestly leaders because food cooked by them was acceptable to all the other castes.
Caste is very generalised and the more important social unit tended to be the jati- sort of like a sub-caste. There could be hordes of these and intermarriage was possible to a certain extent.
If you want a well-written layman's overview of caste in India try
Vishnu's Crowded Temple