Yes, both Asana and Zendesk Support offer a Free Trial.
Asana is designed for Large Enterprises, Medium Business and Small Business.
Zendesk Support is designed for Large Enterprises, Medium Business and Small Business.
Pricing for Asana Starts at $6.92/user/month when monthly whereas for Zendesk Support Starts at $19/user/month when yearly.
Some top alternatives to Asana includes Quickbase , Smartsheet, ClickUp, Zoho Projects, Jira, Basecamp, Trello, Wrike, ProofHub, monday.com, Teamwork, ProjectManager.com, Microsoft Project, Quick Base and Height.
Some top alternatives to Zendesk Support includes Zoho Desk, Tidio Helpdesk, Deskero, Support Hub, HelpDesk, Desky, Help Scout, Salesforce Service Cloud, ReadyDesk, Sitehelpdesk, HESK and BoldDesk.