I'm not an expert in SharePoint but what I know that SharePoint 2013 Foundation Edition is free, and I'm developing ASP.NET applcation which will have a portal. I'm wondering Can I user SharePoint 2013 Foundation as my application portal? I'll use this portal to show visual reports (SSRS reports) in webparts, like in Microsoft Dynamics AX it use SharePoint as its portal and call it Enterprise Portal.
Yep, SharePoint can do what you ask for there, except if you have as you say another ASP.NET application, Microsofts general recommendation is to host stuff like that on a server that isn't running SharePoint. You can use still use client side APIs to talk to SharePoint from your other app, and if your app has any APIs you can probably call it from client side code within SharePoint pages.