A: Yes, that fulfillment center represents a physical presence in California. Sales tax must be collected.
E-commerce and sales tax can be a difficult issue for small business owners. The first question you must ask is whether your product is taxable. In most states, any actual goods sold online are taxable. Next, you must determine whether your company has a "nexus" in the state to which you are shipping. If you have a general presence or link to the state you ship to, then you will generally have to pay sales tax in that state.
Your case is pretty simple. Your company has a link to California because that is where you are shipping your products from and most likely maintain a facility there. Therefore, since a "nexus" exists, you will have to pay sales tax for goods shipped to California addresses.