Will it have the any recurring cost for JS library, or it will be the lifetime free once I will purchase the module from Odoo Apps store?
Your module functionality is limited to projects, or I can also use it in any other module as well?
The Odoo app is paid for every Odoo version, so if you buy for Odoo v.16 you only need to pay when you upgrade to Odoo 17. The JS library / source code is not included. If you want that (to make more serious customizations), you need to purchase it here: https://bryntum.com/store/gantt/