Some drivers, also collecting unemployment, are reporting every dollar paid to them as gross earnings. Is that correct? Should they be able to deduct IRS car expenses from that figure? I know cost of goods sold may be deductible before reporting gross earnings, but am unsure how that shakes out for a service worker. How would this change if they formed an LLC and reported all income through it? Can they form one now and claim all 2016 income through it?

Taxpayers report gross income, which is basically all income received for services performed. They then deduct ordinary and necessary business expenses. This is reported on Schedule C for unincorporated businesses and single member LLCs. So to answer your question, it does not matter whether you are an unincorporated business or a single member LLC.