“In California, who is required to maintain an existing roadway easement across my neighbor’s land that allows access to my house? And as the user of that easement, can the owner of the land stop me from improving the road and from removing blackberry bushes on the easement that create a fire hazard and grow over the roadway?”

First, read the document (usually a deed, sometimes an agreement) that created the easement. Sometimes, it will specify the extent of the easement and the maintenance responsibilities.

Failing that, the general rule is that maintenance responsibility is proportional to the amount of use. If only you use the easement, maintenance is your responsibility; if your neighbor uses it too, you need to figure out a fair way to measure what percentage you use it, and your maintenance obligations will be the same percentages.

As for improvements–again, if the document doesn’t say–it’s a reasonableness standard. Clearing brush that’s a potential fire hazard is probably reasonable. Paving a previously-unpaved road may or may not be, depending on the circumstances. For something like that, it’s probably best to approach your neighbor in a very neighborly manner.