What properties do you have defined for pdfs and other page files that are missing from the media gadget? Could you post that code you used for vpp migration tool?

Referring to something like this: 

[ContentType(GUID = "BB0099B6-5C65-4D37-9812-ED0D3E12BC2F")]
[MediaDescriptor(ExtensionString = "pdf")]
public class PdfMedia : MediaData
{
   public virtual int MyProperty { get; set; }
}

I've tested both without a dedicated class for PDF, and with a dedicated class "PdfMedia" as the example you send.

I had an error first time I run the migration-tool with sitepagefiles ( an strange error "The component with of the type SiteSeeker.EPiServer.EPiServerNotificationManager was not registered with the container").

Is it possible to re-run the migration? Which steps do I have to take if it's possible?

You should just be able to re-run the migration as the tool will only process files that have yet to migrated.

If you want to start a fresh re-run of the tool, you can revert to a DB backup copy that wasn't touched by VPP migration and you can delete or backup the current blobs folder. Then run vpp migration tool after that.

I haven't seen that particular error message before, unfortunately, but looking at error seems to complain about some siteseeker reference(s).