Senku's general knowledge, plus his access to proper tools, means that he can methodically disassemble and study the individual components of the drone carefully. It's good enough that he could reasonably put the drone back together in the same state he found it in if he wanted to, or salvage its individual components and use them for something else. This includes the exterior hardware (motors and rotors, metal chassis, four small cameras, stun batons and their individual capacitors) as well as the interior bits (the large gripping claw used to pick up its victims, a spring-loaded medical syringe - empty of any material, interestingly - and heaps of wires, circuit boards, and all kinds of other electronic bits).

The first thing Senku is likely to notice from his teardown is the answer to that third question, which is that the construction of this drone is really weird. Parts of it are made with technology that could reasonably come from modern-day Earth, but other parts of it don't have any kind of recognizable Earth tech analogue, and the merging of the two seems to happen at random. It feels makeshift - expertly constructed, yes, but still noticeably improvised.

Power seems to have come from a set of rechargeable batteries that are secured to the underside of the drone's chassis roof, connected to induction chargers on the outer edge and all of the internals on the other. Senku can figure out pretty quickly that all of them are useless, having been overloaded thanks to Operation Squirt the Drones and Their Pads. The batteries and all electronic components related to their regulation are basically scrap (which incidentally answers your second question: Yes it could theoretically be fixed, if these components were all replaced with something that actually works).