You will need fishing license for what you want to fish. 1 day and I think 3 day license. Going on a limb here, but depending what camping area, national forest I think good, camp sites, not good. Someone with more knowledge will be along. Details of camping area might help...bump for visitor...

Almost all the Redwoods, Coastal or Giant are in National, State or shared Parks.  Parks all have relatively tight regulations on carrying weapons.  I can't think of where or even why you might want to carry a lever rifle or any rifle in any of the parks.  (OK, there might be some areas near some of the coastal groves where you might wander in to a marijuana gow.  Although, very few of those are close to the parks.  As far as needing to shoot a bear or deer attacking you.  Well if you shoot a bear in a park, save the last bullet for you, it will be easier for everybody concerned.

belt knifes shouldn't be a problem, again comes down to why?  hatchet, fine in your campsite.  You can't gather wood except in very limited circumstances in the parks.

The Redwood Parks and most areas around those parks are pretty benign.  Now if you start talking about some of the urban parks or out in the desert, the story is different.  The rules are the same, the recommendations aren't.  I'm not going to say I carry in some of those areas, because I don't have a carry permit.  But I always have little friends and maybe a big friend around in the desert.

You probably need to try and make camping reservations as soon as possible.  The larger redwood country parks fill up quickly.  Some of the smaller ones might not.  If it is school vacation time, going to be tough.  Prairie Creek Redwoods is one of my favorites, but I've only camped there in the off-season.  Cold and rainy, well cold and rainy for a Southern Californian.

McArthur-Burney Falls State Park has a nice lake and impressive waterfall.

https://oag.ca.gov/firearms/travel
https://www.parks.ca.gov/?page_id=21301

That said, I've never been asked, well not recently that I recall, about having guns in the car when entering any parks.  Maybe years ago at a national park.  It's still a bit of a mash-up as parks/reserves can have different rules depending on the location.  For example, I was recently in NorCal and saw buildings marked for no ccw at a National Park (Seashore) but don't recall notices at all at a State Reserve or Park.

Once on the AG's site, it might be worthwhile to check out the other restrictions on things like magazines, etc., just in case.  If really considering "needing" something, instead of a lever gun, there's always the possibility of a "featureless" rifle as well.  That could be as simple as  a grip paddle(?) precluding  thumb wrap around and/or a properly configured "stock," including pinning or fixed length stocks, etc.  Remove any forward pistol grip, flash suppressor.  I'd go with a thread protector instead of muzzle brake, swap them back again on departure.  Stick to 10 round mags.  Also, "gasp," a Mini-14, M1As (with CA brake) or M1 might be less bother.

I'm not sure when it took effect but one of the recent law changes, I believe, requires locking/fixed containers for firearms left unattended in cars.  Not sure the details and probably a good idea anyways, some "park" areas are well known for smash and grabs, etc.  Probably something to check while at the AG site.  That comes at least partially from a high visibility murder not too long back when a person was killed with a handgun stolen from an LEO vehicle.

I think you will see that there are lots of pocket/belt folders out and about but few fixed blades and unlikely to see anyone carrying an ax when not actively dealing with firewood.  Which can't be gathered in most parks and often they want to be purchased locally to avoid pest problems.