How to Know if I have A Restricted or Full Access to Table
Basically, are there ways of knowing if I am viewing a full table or
  just a view derived from it?


The only thing you can see if you have restricted permissions is the type of object:

select type_desc
from sys.objects
where name = 'yourObject'


If you have only permissions on a subset of columns, you'll never figure it out using metadata (system tables/views):


  The visibility of metadata is limited to securables that a user either
  owns or on which the user has been granted some permission.


Related link:
Metadata Visibility Configuration