I've heard there are a host of new laws in CA this year and I haven't really kept up with them. I live in NV and drive to LA a few times a year to visit my family for the holidays. I typically take a pistol with me, mag capacity under 10 rounds, and keep it locked in a lockbox unloaded in the car. Obviously I am bringing loaded mags also... is this an issue with the new ammo laws? I'm a NV resident with NV plates and if i'm driving in CA with gun/ammo in the car it is only while travelling into or out of the state.

Loaded mags are no problem, even on your person. Pistol unloaded in any locked container other than a utility or glove box is fine. Ammo import ban doesn't apply to non-Californians if for personal use. For your situation, nothing's really changed (yet; I'm sure we're getting boned again this session).

Topic is of interest to me. So I have to keep my pistol in a locked case rather than the glove box or centre console but keeping a mag or tow on my person is fine?  Capacity limit is 10 rounds?

Pretty sure my AR's are all far too scary for CA, so what are the rules for a shotgun?

For whatever reason there is no sticky for travel issues for California.  So the answers are dug up, posted and discussed frequently.  Here's the Ca. DoJ website on travel.

https://oag.ca.gov/firearms/travel

There are some things to consider.  It's clear that one can't use a glove compartment.  It's not entirely clear what a "utility" compartment is.  One also has to observe the magazine capacity laws (10 and under), nor can one "import" an assault weapon.  Those are defined in other places.  Also, one should be aware of/wary of potential problems transporting a firearm to/from the vehicle to avoid stumbling over "open carry" or similar violations, etc.  For example, a rifle or shotgun is not required to be in a locked container in the vehicle, but, you can't "open carry" it (in general terms).  So a casual popping open the trunk and schlepping a long gun from the car to the lodging place, etc., is not a good idea,.  It's really not difficult.

The first question is, is it a pump or semi-auto?  Just for clarity, it has a smooth bore, correct?

Smooth bore pump

As it is not a semiautomatic, center fire rifle and does not have a detachable magazine, none of the assault weapon laws apply.  There is still the federal law on minimum overall and barrel lengths but you most likely already meet those.

thanks. What really pisses me off about CA is the magazine size restriction doesn't have a specific allowance for military. I frequently find myself needing to go to CA at the end of a drill day at the armory, and its completely out of my way to go home before heading there. I don't have a gear locker, so that means all my TA50 I need for the weekend is in my car, obviously including my armor with all my issue mags on it. So now I have to go all the way home to put away my issued gear, because it is illegal in your state.
I've had various people tell me LE in California would never arrest/charge someone in this circumstance, but I honestly don't trust them at all. Lets say I get in a car crash on I-15 and CSP shows up and there's magazines everywhere, I find it hard to believe they're going to just say oh hey no big deal and roll out.

Zero fucks given for your trivial problem of inconvenience.  We are living with this all day, every day.

P.S.  Were I you, or offering advice to you, I would obey the laws and assume they will be enforced.

I'm pretty sure that there is in fact an exemption for military when it is for duty purposes.

The way they wrote the law it is only clear it covers while you’re on duty. The language is vague enough that I feel I need to stay on the side of caution.

I'd suggest sweet talking someone into letting you leave them at your drill site.  How many empty mags are you talking about?  (Empty because I'd guess that storage of live ammo would be an additional set of hoops and headaches.)  This isn't an on-duty situation.