caravans & Roads

I have a couple routes to other civs not too far but through hilly tiles. Is it worth it to build roads to the borders for them to travel faster?

it's a bit confusing that you labeled this thread with "g&k", but anyway:
caravans/trade routes are not "faster" with roads, they just extend their range. so you might be able to reach more cities if you build roads

Nope,

1) while the caravan unit itself would travel faster on roads it wouldn't effect the food/hammers/gold rate.

2) while a road also extends caravans range, each and every caravan is a waste of a trade slot that would be better as a cargo ship, given that cargo ships provide 2X the stuff caravans do.