Once after the plugin purchase, you will get an email from LearnDash along with the Download link & activation key. Refer this for installing LearnDash plugin - https://www.learndash.com/support/docs/getting-started/installation/
No, LearnDash does not offer any free trial or plan. If you want test LearnDash, then make use of their 15days money back gauarantee, you can request for full refund if you are not satisfied with LearnDash. If you are looking for best LMS plugins here is the list.