Do they have lockers there?

Yes they do.

Yes they do. They are located on Buena Vista Street in California Adventure. There are also locker options in the esplanade just outside each park entrance. Disneyland Daily has a map on her page showing the locations of the lockers. Highly recommend checking it out. https://disneylanddaily.com/the-logistics-of-disneyland/#Lockers

Yes, I believe they do.

yep, they might be hard to find but just ask a park worker and you'll be good