Regarding transportation of firearms:
Pursuant to California Penal Code section 25610, a United States citizen over 18 years of age who is not prohibited from firearm possession, and who resides or is temporarily in California, may transport by motor vehicle any handgun provided it is unloaded and locked in the vehicle’s trunk or in a locked container. Furthermore, the handgun must be carried directly to or from any motor vehicle for any lawful purpose and, while being carried must be contained within a locked container.
Pursuant to California Penal Code section 16850, the term "locked container" means a secure container that is fully enclosed and locked by a padlock, key lock, combination lock, or similar locking device. This includes the trunk of a motor vehicle, but does not include the utility or glove compartment.
Regarding importation of ammunition into CA: From what I understand, the law is inclusive of CA residents. I don't see any restrictions of Texas residents bringing ammo into CA.
Look at exemption (b)(13)
CA Penal Code 30368. (a) Commencing July 1, 2019, a resident of this state shall not bring or transport into this state any ammunition that he or she purchased from outside of this state unless he or she first has that ammunition delivered to an ammunition vendor in this state for delivery to that resident pursuant to the procedures set forth in Section 30366.
(
b) Subdivision (a) does not apply to any of the following bringing or transporting into this state any ammunition:
(1) A firearms dealer licensed pursuant to Sections 26700 to 26915, inclusive.
(2) A person who is on the centralized list of federal firearms licensees maintained by the department pursuant to Article 6 (commencing with Section 28450) of Chapter 6 of Division 6.
(3) A gunsmith as defined in Section 16630.
(4) A wholesaler as defined in Section 17340.
(5) A manufacturer or importer of firearms or ammunition licensed pursuant to Chapter 44 (commencing with Section 921) of Title 18 of the United States Code, and the regulations issued pursuant thereto.
(6) An ammunition vendor.
(7) A person who is licensed as a collector of firearms pursuant to Chapter 44 (commencing with Section 921) of Title 18 of the United States Code and the regulations issued pursuant thereto, whose licensed premises are within this state, and who has a current certificate of eligibility issued by the Department of Justice pursuant to Section 26710.
(8) Authorized law enforcement representatives of cities, counties, cities and counties, or state or federal governments for exclusive use by those government agencies if, prior to the importation, the person has written authorization from the head of the agency authorizing the acquisition of that ammunition. Proper written authorization is defined as verifiable written certification from the head of the agency, or designee, by which the person is employed, identifying the employee as an individual authorized to acquire and import ammunition, and authorizing the transaction for the exclusive use of the agency by which he or she is employed.
(9) A properly identified sworn peace officer, as defined in Chapter 4.5 (commencing with Section 830) of Title 3 of Part 2, or properly identified sworn member of a federal law enforcement agency who is authorized to carry a firearm in the course and scope of the officer’s duties.
(10) A contract or common carrier or an authorized agent or employee thereof, when acting in conformity with applicable federal law.
(11) A person who purchases the ammunition from an immediate family member, spouse, or registered domestic partner if the person brings or transports into this state no more than 50 rounds.
(12) The executor or administrator of an estate that includes ammunition.
(
13)
A person that at the time he or she acquired the ammunition was not a resident of this state.
(14) Ammunition that is imported into this country pursuant to provisions of Section 925(a)(4) of Title 18 of the United States Code.
(15) A licensed hunter who purchased the ammunition outside of this state for use in a lawful hunting activity that occurred outside of this state if the person brings or imports no more than 50 rounds into this state and the ammunition is designed and intended for use in the firearm the hunter used in that hunting activity.
(16) A person who attended and participated in an organized competitive match or league competition that involves the use of firearms in a match or competition sponsored by, conducted under the auspices of, or approved by, a law enforcement agency or a nationally or state recognized entity that fosters proficiency in, or promotes education about, firearms, and the person brings or imports into this state no more than 50 rounds of ammunition designed and intended to be used in the firearm the person used in the match or competition.
Informative video here:
https://www.youtube.com/watch?v=zsb0RRw72xw