#shift timings

Yes, the FAA has regulations limiting the flight time and duty period for commercial passenger operations, flight instruction and fractional ownership operations (basically private jet clubs like NetJets).

Services provided by Air Ops like search and rescue, aerial firefighting count as part of general aviation, hence not subjected to FAA rest requirements.

Crew fatigue is a danger to flight safety whether you're a commercial pilot or not, so it's up to individual agencies to set their own duty time limit. According to this interview with a real LAFD pilot, they work a traditional 24/48 firefighter shift schedule, and there's no hard limit set up for maximum hours per flight, but they try keeping it under 6 hours for the initial phase. If the mission is expected to last much longer, they'll start calling more people in (probably why Tommy had to leave the bachelor party) and enter crew rotation. After their first 6 hours, they'll have a rest period, from 4-8 hours, before they can go into the air for another 4 hours, rinse and repeat, until the fire is out. For those large scale campaigns, crew members can be on duty for consecutive days.

For typical operations though, while your department might advise against working back-to-back shifts for 48 hours straight, it's absolutely not against any regulation. You're likely spending most of your shift on the ground on a regular day anyway.

It's not the US, and it's a special case, but air crews of the Air Greenland search and rescue unit work a whopping 2-week shift schedule. Yes, one shift lasts for 2 weeks, 24/7. It's up to individual member to decide if they're fit for flight or if they need rest.

They once worked 12 hours a day for nearly a week to evacuate the residents of a settlement afflicted by a tsunami in 2017.

Source: Vertical Mag

I tried to find more information about this but literally no one at Air Ops is talking working hours on the net. All I got is a limitation on maximum flight time for helicopter pilots in the US, i.e., 8 hours for 1 pilot and 10 hours for 2 pilots followed by 10 hours of rest. However this is for normal duty and in emergency situations, they can go for 12 hours, exceeding which, they are eligible for an hour of rest for every half an hour of exceeded time. Now, I have no idea if this applies to LAFD Air Ops as well but I did find this one LAFD pilot, in an interview, talking about how during a series of fires, he had to fly for 8 hours periods at a stretch with 2-hour breaks in between for 4 or 5 days in a row.

There are no separate rosters given for air ops and LA County, as far as I know, works 24-hour shifts so it could also be that during normal shifts, they still do 24 hours but only fly for a limited period and spend the rest on maintenance or ground duty.

P.S - If you're looking for what kind of helicopter accidents can happen while fighting fires, I did find this article.