Move a site hosted on IIS/MS SQL Server across to LAMP stack
There shouldn't be any issues as such if you properly follow the steps of Migrating a Drupal Site. You can find detailed steps on How to Migrate a Site.

This documentation provides a detailed documentation on Backing up and migrating a site.

Regarding taking a database backup of Site, you can checkout Backup and Migrate Module for quick and easy database backup of site. Here's how you can quickly setup Backup and Migrate module and backup your site databse.