The State of California and the National Park Service operate under a cooperative agreement or possibly a memorandum of agreement. I don't have time to look for such a document. It would list who will do what, including the Redwood NP protection rangers using the VHF radio system and the state's "Northern" dispatch center in Folsom, California. They likely scan the park's net, but use this dispatch center for status tracking, receive calls for 911 incidents, getting BOLO' and for vehicle/people license, want/warrant information. This park is likely a concurrent jurisdiction enabling state park rangers to enforce state laws on Redwood NP land as these rangers are state peace officer designated. I would think NPS protection rangers are deputized state peace officers as well. How this affects daily activities for each would be spelled out in the coop agreement and in operating plans that could be annually prepared.
Each agency cannot delegate the land management to each other. Sometimes they share positions, such as geologists, botanists, foresters, soil scientists and similar. These specialists are staff, with no line authority, so they can accomplish evaluations/research and write reports for the line officers in each jurisdiction to make decisions. They can also share on the ground crews for such purposes such as hazard tree removal, road and facility maintenance (plumbers, electricians, carpenters, painters and the like) and fuels treatments. This is spelled out in the agreement and to a level of detail that makes reading agreement documents tedious to those not involved.
For SAR I would think that the park has resources, but may also need the assistance from Humboldt and Del Norte Counties sheriff's office sponsored volunteer SAR teams.
The Cal Fire Humboldt-Del Norte Unit is dispatched by the Fortuna Emergency Command Center. Cal Fire does not show up on the WildWeb CAD system. Federal land management agencies that are co-located with Cal Fire, such as the Camino ECC, don't always show up on WildWeb. So in the case of Camino we don't get to view the CAD for the Eldorado National Forest. The same is the case for the Susanville ECC and the Lassen NF. However, the ECC for the Fresno-Kings Unit is co-located with the Sierra NF dispatch center. The Sierra NF shows up on WildWeb.
The same is true for the Monte Vista ECC and the Cleveland NF showing up on WildWeb. I'm not sure of why this is the case.
For fire, I don't see the state relieving themselves of responsibility for state land, which in the case of state parks, is always in the State Responsibility. Small remote parks that are surrounded by federal public lands can have wildland fire protection provide by a federal agency under a coop agreement. However, in this case Cal Fire has nearby non park, non public lands in the State Responsibility Area (SRA) so they likely provide protection. This subject to a multi-layer set of cooperative agreements that fire has. The USFS Six Rivers NF, Redwood NP, Cal Fire and local departments operate under the closest resource principle that works outstandingly in the fire service. The Six Rivers NF, Redwood NP and Humboldt Bay NWR used to use Cal Fire's Fortuna ECC, but in the the last couple of years withdrew and formed the "North Coast Interagency Communications Center" located in the Six Rivers National Forest Supervisor's Office in Eureka. In the event of a fire that has federal and state/local resources responding, the lead dispatch center for the incident is determined by the land ownership. All resources are dispatched on their corresponding nets that includes an announcement of the command, tactical and air to ground frequencies to use. Each resource then advises their dispatcher of switching to other nets, if they are responding to a different agencies' protection area.
If a fire is on SRA then utilizes the Cal Fire local net (Humboldt-Del Norte 151.2500), 3 repeater sites in the area for both Cal Fire Command 1 (151.3500) and Command 2 (151.2650), ground tacticals (Tacs 3, 7 &10), Air to Air Tactics (Air Tac 6) and air to ground (AG 3) frequencies. Redwood NP and Six Rivers NF units just switch over to radio groups with these frequencies loaded in them. Fortuna then becomes the all important "ordering point," which becomes the dispatch center that gets everything the fire needs. This Cal Fire unit is designated for Command 8, but my older information shows all the repeaters on it are located south on the Mendocino Unit.
The opposite is the case if resources are responding to a Redwood NP fire where the North Coast Interagency Communications Center takes the lead and ordering point responsibility. The command frequency would then be the Redwood NP net, with federal tacs, air to ground, air to air tactics (FM) and air to air (AM) frequencies pre assigned for initial attack. Some of these are assigned on a dispatch area or initial attack zone basis. Air to ground primary would be AG10 primary (167.6000) and AG08 secondary (166.8750), air to air (FM) would be Air Tactics 61 primary (166.5625) and Air Tactics 44 secondary (168.8375) and air to air (AM) would be 118.950 primary and 128.250 secondary. These are the same AM frequencies that would be used on Cal Fire incidents as well. I don't know what tacticals are assigned for federal incidents other than the Six Rivers core frequency plan includes NIFC Tac 2. For a significant initial attack on federal lands the Six Rivers has a Service Net (169.9500) at four repeater sites, that could be used for Redwood NP as well if they have coverage in the park as well. If an incident moves to an extended attack managed by a local Type 3 Incident Management Team (IMT), then local frequencies are used nearly every time. Of course, if the incident grows in size and complexity where a Type 1 or 2 IMT is used the NIFC system will arrive shortly.
No matter the jurisdiction all wildland fires end up getting coordinated by the Geographic Area Coordination Center, which in this case is the Northern California GACC. What you should understand is that when the fire bell rings, all the departments and agencies mold into a single unit. The Incident Command System is the glue in this mold.
I'm not sure if I've answered all your questions, but this is likely a good start.
