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The first question is by far out of scope from my knowledge. Reading the German Wikipedia articles de:Veda (the English text is very similar Veda) on it my understanding is the following: there are four vedas (Rigveda, Samaveda, Yajurveda, Atharvaveda). Bhagavad Gita is in the English and German Wikipedia articles listed under ""other scriptures"" and Smriti, respectively. From my limited understanding I would conclude that the text is not a Vedic text in the narrow sense of ""Vedic"". 
However, it seems to me that the term ""vedic"" sometimes is used in a broader sense, basically meaning something like ""knowledge"". In this sense it might be possible to classify the text as ""vedic"".
From what I read from a few more sources I would not put it under ""vedic text"", but as I said in the beginning I know so little about these things that no one should rely on it ;-)
Mmh, better I start thinking about your second question ...
best regards   "