is there a minimum franchise tax of $800 for S-Corporations in California?

Answer 1

Yes. The following is an excerpt from CA tax law:

Minimum Franchise Tax:

Except for newly incorporated or qualified corporations,
and unless otherwise exempted by law, all corporations
incorporated, qualified to do business, or doing business
in California are subject to an annual minimum franchise
tax. The minimum tax is $800 per year, except for certain
inactive gold mining corporations and quicksilver mining
corporations that pay a minimum franchise tax of $25
per year.

Except for newly incorporated or qualified corporations,
if the corporation is inactive or operates at a loss during
any taxable year, whether or not a full 12 months, its tax
for the taxable year is the minimum tax.

Hope this helps :)

Answer 2

Yes