Are you using SharePoint Online or SharePoint Server?
Please see the answers below for SharePoint Online:
1 You can export the items from Recycle Bin using PowerShell. Please see the sample script below:
#Get the PnP PowerShell module
##Skip this line if you already have it
Install-Module SharePointPnPPowerShellOnline
#Config Variables
$SiteURL = "<siteURL>"
#Connect to PnP Online
Connect-PnPOnline -Url $SiteURL -Credentials (Get-Credential)
#Get Recycle bin Items
Get-PnPRecycleBinItem | Select Title, ItemType, Size, ItemState, DirName, DeletedByName, DeletedDate | Format-table -AutoSize
#Export results to CSV
##This is the path where you want to export this file
Get-PnPRecycleBinItem | Export-Csv C:\restore.csv
Reference: SharePoint Online: Search Recycle Bin using PowerShell.
2 PnP PowerShell does not support restoring items from csv file. See a reference here: Restore Recycle bin SharePoint Online with PowerShell.
If you are familiar with CSOM (Client -Side Object Model), here is a sample script you can take a look at: Restore SharePoint Item From Recycle Bin Using PowerShell.
3 It is not possible to restore the documents to different locations for the time being.