GM, how plausible/reasonable would these relic concepts be?

1) A thermal borehole complex tapping the core of a barren world. While the facility itself is inoperable due to ancient active safety measures, concepts and technology derived from it enable lesser yet effective imitation thermal tap facilities for greater resource and clean energy production.
2) A ancient titan-size starship found floating in the asteroid belt. The ship is ruined beyond restoration or understanding of it's origins, but technology derived from it in the fields of gravity control, structural integrity, and self-repairing materials enable widespread mega-scale engineering and building very big.
3) A ancient sensor hub connected to a hidden network of nodes across the sector. Actually processing the flood of information coming in is a problem however, and dependent on finding and restoring the sensor relays to extend the sensor's reach.

Also, what is a good ballpark measure for starting spacefleet forces? I like to err on the side of caution when it comes to initial fleet sizes.