Regarding your specific questions, you can add billable hours and expenses and tag existing transactions to projects. After making adjustments at the end of the project for your estimated vs. actual work, you can run reports to see your profitability. The challenge will be adding budgets - as it exists at the moment, you can add transactions and expenses, but there isn't a direct budgeting feature.
You might consider creating a specific "Project" account and tie all associated costs to it (i.e. deposit the budget amount as the opening balance and subtract from there).