Every nuclear power plant in the US has an NRC mandated Safety Parameter Display System. These were retrofitted after the TMI-2 meltdown. The SPDS is supposed to provide a concise view of critical parameters to avoid the sort of confusion that led to the TMI-2 incident.
In 2003 Davis-Besse had its SPDS disabled by SQL Slammer, a worm that congested the network on the site. So in answer to your question, yes these 1970s plants do indeed have devices interconnected in the contemporary manner, and compromises of these networks have already produced reportable events.
The core components of our power reactors are not at the mercy of software; operators have authority over reactor protection systems that are deliberately independent of complex digital controls. Nevertheless, a clever attacker could probably engineer enough confusion or interfere with ancillary systems badly enough to produce a notable incident such as a SCRAM. That would certainly make headlines and lead to a prolonged investigation.
Is it possible that greater damage could be done? Anything is possible. If so I'd imagine it might involve cooling pools, their circulation and alarms... who knows. Given enough time, knowledge and planning it might be possible to cause a serious problem.
It depends. Fission is complex. Factors include reactor design, fuel age, xenon accumulation, which parts of the RPS tripped, whatever axles the resident NRC inspector(s) wrap themselves around... those are few I can think of as a layman.
"Do they have any sort of fast recovery procedure?"
While operators do strive to minimize outage there is no general "fast recovery" procedure. There is a startup procedure and that's what you follow. If everything is optimal then 12-ish hours to begin the restart, several hours thereafter to become critical, then a relatively slow process of pulling rods until full power is achieved. "Hot xenon" startups are something you study and practice in a simulator.
The military has other prerogatives and naval reactors see rapid and frequent transients. Naval reactors are built (at great expense) to do this. They're also smaller than civilian power reactors; a 165 MWe naval reactor being thought "large" whereas a 600 MWe civilian power reactor is on the small side.
Non-safety-critical components in the steam plant are likely to have networked PLC control. While nuclear probabilistic safety assessments support that licensed reactors can safely endure casualties involving such components, the safety system is subject to failures and crippling the plant and causing a reactor transient is likely a good enough result.
