Is it possible to to add custom fields to FeedItem object? Also where can I see the object and its fields (apart from documentation) inside salesforce platform.
Unfortunately you cannot edit FeedItem. You can't see the object itself, but you can manage settings related to Chatter such as triggers on FeedItem under Setup->Customize->Chatter.
If you're interested in seeing the properties of FeedItem I suggest checking out workbench. The Standard and Custom Object section under Info is invaluable.