My team wants to take data from Salesforce and using Integration Services, integrate that data to another platform.
First of all , I would like to know if this is possible, and if it is, is there any documentation that I could use as a guide for this
Yes, this is possible and that you don't need data loader here. Data Loader is a tool that you use to import/export data to/from Salesforce.
What you are really looking for is a data integration between Salesforce and an external system using APIs. You can integrate either using APIs exposed by Salesforce or can integrate your external system using ETL tools. It depends on how you want to integrate data, real time or batch, but either of these approaches will help you achieve this.
The Lightning Platform API Basics trailhead is good place to get started on this topic.