Endless Excavation give you tools production +1 relic per scouted province .
1. Is that relic random or ... ?
I’ve got this wonder and so I tested it for you. Finishing scrolls province gave me bonus scrolls relics. Finishing elixir province gave me bonus elixir relics. Therefore it’s reasonable to assume that the
bonus relic is not random, but it
fits the province type.
2. Will you get the relic if you don't have street connection ?
That I won’t test for you, especially because I’m running out of provinces due to long scout times.
However, only plain culture and population stats of a building work without street connection. (Example: If you disconnect a residence, you will still get the population, but the building won’t be generating any coins.) It’s reasonable to assume that without street connection you get no bonus relic (and no supplies).