I only have about 25 hours of Sikorsky time, in an SH-60S Knighthawk, the latest navalized version of the Blackhawk. The auto flight functions were not what you would see in a Fixed Wing Airliner or Business jet, but they do have the ability to hold attitude, altitude, heading and airspeed with automation. I can't speak to the S-76, but I would assume that similar functionality has to be in place to allow for single pilot operations like you reference above. I do not know if they have the ability to program a climb or decent or turns along a route like most auto pilots that you see in fixed wing aircraft can. I will say, now flying an Airbus 320 for a living, that I look back on the way we flew light attack helicopters and think that we did not use our automation near enough, especially at night or in bad weather. Most helicopter pilots are very adamant about wanting to "fly" their aircraft, rather than simply manage the automation.
Trying to answer your second question....On the last helicopter I flew regularly, the UH-1Y, we have an auto flight mode called "cruise hold" which would maintain all flight parameters and could not be "pushed through" by manipulating the controls, you had to deselect it first, then manipulate the controls. Cruise hold would also turn off if you lost power from one generator (which is tied to an engine) or received a primary (very serious) Warning indication associated with a major systems failure or issue. Helicopters are weird beasts relative to fixed wing aircraft in the sense that fixed wing airplanes generally keep doing what you told them to when you turn off the automation or let go of the controls. Helicopters tend to hold their previous attitude for a shorter amount of time and start something different if you aren't actually controlling them. So, I could certainly see a scenario where the (single) pilot was using an auto flight function to assist him while he was looking at the map to manage airspace and terrain and then had it kick off, either through an inadvertant switch actuation or some sort of emergency and that would make a recovery more challenging, especially in or around clouds that prevented you from having high situational awareness about the terrain or traffic.
They teach you in safety school that eyewitness accounts about aircraft mishaps are largely worthless. Where they do have value is in context. So, when the guy on the ground tells you that he saw the aircraft smoking and spinning with people leaning out the windows screaming through clear skies before it hit the ground, the only really valuable piece of information is that the aircraft was clear of clouds in a decent. It also gives an investigators a flight path angle they can build based on the locations where witnesses saw the aircraft relative to where they were standing. Of note, I imagine the NTSB guys are canvassing the neighborhoods around Calabasses asking for doorbell and security camera footage from homes and businesses. A recent crash or an Atlas 767 in Houston was captured on a school field house security camera video and that video helped confirm several things for the investigators. I wouldn't be surprised if there is a video of part of the terminal flight path for this aircraft.
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https://www.houstonchronicle.com/news/houston-texas/houston/article/Video-shows-final-moments-of-doomed-Atlas-Air-13655569.php)
@barbed wire Bob answered this really well in post #1023. To address what to do when you punch in to the clouds unexpectedly, it is very relative to where you are. Many military IIMC procedures emphasized doing a 180 degree turn to go back the way you came with only slight altitude deviations to keep members of the flight from hitting each other. As an alternate procedure, for when turning around doesn't make sense (ie. target area egress) your IIMC procedure would have the aircraft break up in a fan pattern to ensure separation, but with only minor altitude deviations for deconfliction. In terms of climbing in this situation, the pilot doesn't know what is above them traffic wise, especially in the insanely crowded airspace around the Los Angeles area. Also, on the southwest bound heading that the aircraft was on after clearing Van Nuys airspace, they were getting very close to the 5000' shelf of LAX's airspace, so they had a limited amount of vertical space to work with. When you are airborne and attempting to transition from VFR (visual flight) to IFR (instrument flight) part of the implied contract with ATC is that you will remain VMC until ATC says your call sign, declares "radar contact" and gives you a clearance. If you go IMC and then call ATC asking for help, you are essentially declaring an emergency, and might even hear as ATC's response, "are you declaring an emergency? " followed by "are you VMC now?"