I have implemented a custom FBA solution in SharePoint 2013 
using this link <http://sivarajan.me/post/sharepoint-2013-custom-claims-fba-based-mixed-mode-authentication-part-1>

1)FBA users got "sorry this site has not been shared with you"

I followed the below steps and now all fba users can view the site 

 - On Central Administration, navigate to Application Management -> Under Web Applications: Manage web applications
 - Select your My Site -web application by clicking it, and open Permission Policy
 - Click Add Permission Policy Level
 - Enter at least the Name for your Permission Policy
 - Select following Permissions:

    **Create Subsites**  -  Create subsites such as team sites, Meeting Workspace sites, and Document Workspace sites.

    **View Pages**  -  View pages in a Web site.
    
    **Browse User Information**  -  View information about users of the Web site.

    **Open**  -  Allows users to open a Web site, list, or folder in order to access items inside that container.

 - Leave other parts unmarked and click Save

 - Make sure your My Site -web application is selected and open User Policy

 - Click Add Users, and on first view leave Zones: (All zones) selected, then click Next >

 - On Choose Users -part click Browse (the catalogue type of icon). Click All Users and select Everyone activated. Press Add -> and OK

 - On Choose Permissions, select the Permission Policy you recently created

 - Click Finish

I have 3 documents libraries directory under the root 

partners.contoso.com/documents1
partners.contoso.com/documents2
partners.contoso.com/documents3 

I have following FBA users test1, test2,test3 

When test1 logs in it should only be able to see documents1 
test2 --> documents2
test3 --> documents3 

I have not implemented the asp.net role manager as I am controlling that in SharePoint user group  

When test1 logs in it is able to view all the document libraries (documents1,documents2,documents3) 

Is it because asp.net role  is not implemented ?

Thanks