My LLC is currently not making any money and I just want to avoid paying the $800 fee California charges annually. Again I have no business assets currently in CA and my business is 100% online. The question is 1) can I operate the LLC without registering a foreign LLC and 2) can I still claim some of my business expenses on my tax return?
A single member LLC by default is a disregarded entity for federal income tax purposes. Most states conform to federal rules; California is one of the states that conforms to the federal check the box regulations. See attached:
https://www.ftb.ca.gov/businesses/structures/llc-filing-requirements.shtml
As a result you will need to file form 568 and pay the fee as you are doing business in California; regardless of where you may have originally registered to do business.
Attached is a link for some additional discussion from the Franchise Tax Board:
https://www.ftb.ca.gov/businesses/Structures/Limited-Liability-Company.shtml#filing_guidelines
The $800 is the minimum franchise fee. Franchise fees are paid regardless of whether the entity is making any money as it is a "privilege tax"; the privilege to be able to conduct business in California.
Revenue and Taxation Code (R&TC) section 23101 was amended to change the definition of doing business in California for taxable years beginning on or after January 1, 2011. Thus, for taxable years beginning on or after January 1, 2011, a taxpayer is doing business in California if it actively engages in any transaction for the purpose of financial or pecuniary gain or profit in California.
Whether you register with the Secretary of State of California will have no bearing on the filing of form 568. Registering to do business in a state is generally determined based on facts and circumstances. One of the big drivers is that if a business is NOT registered in a state then they lose the ability to utilize the state court system.
I would recommend you discuss the later issue with an attorney who can provide sound advice on that matter.