Lansweeper does not currently actively keep track of the time an agent spends on a ticket and store it in the database. This has been requested and is on our customer wish list so that it may get implemented in the future.
As for your second question, there are currently no helpdesk reports in Lansweeper or the report center. We are however working on these and they are getting close to completion and will be added in an upcoming release. There have however already been some helpdesk reports posted in the 'Report requests and questions' section of the forum.