Yes, both Asana and TMetric offer a Free Trial.
Asana is designed for Large Enterprises, Medium Business and Small Business.
TMetric is designed for Individuals, Freelancers, Large Enterprises, Medium Business and Small Business.
Pricing for Asana Starts at $6.92/user/month when monthly whereas for TMetric Starts at $4.16/Month when Billed 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 TMetric includes Timely, clockodo, Time Doctor, Everhour, Toggl Track, TrackingTime, Clockify, TimeTrack, Timesheet and Time Tracker by eBillity.