Yes you can deduct Home Office with 1099 self employed income. You need to fill out schedule C for your 1099 self employment income. Then expenses, such as home office or section 179 depreciation can only be used to reduce your schedule C taxable income to zero, and not to create a loss. Excess deductions for these carry over to the next year. And you have to answer yes to both questions about exclusive and regular use, not just one. The area of your home office must be used regularly and exclusively for business to deduct it.
Here's a bit of clarity for the two questions related to business use.
Percentage of time spent conducting business in the office - This must be 100%. You may only be in that office for one hour a week. But when occupied, it's for business purposes and absolutely nothing else. That's 100% business use.
Percentage of business conducted in that office - Could be less than 100%. For example, if you are a roofer you spend about 70% of your time out of the office nailing shingles. But you spend 30% of your business hours in that office doing things like payroll, ordering supplies, taking calls from customers, etc.