Namaste ShivaFan
As for the Garga Samhita I already commented on Re: LORd SIVA : A Gaudiya Vaisnava Perspective.
The terms "avatara" and "amsa" may be correlated, but not necessarily.
Avatara means "He who descends". Amsa means "a part or portion".
What kind of avatar is Lord Krishna in comparison with other forms of Lord Vishnu you can read in my posts on Re: LORd SIVA : A Gaudiya Vaisnava Perspective.
Regarding Goddess.
The Supreme Lord has His eternal consort or goddess. Gaudiya Vaishnavas say that Sri Radha or Srimati Radharani is eternal consort of Lord Krishna. Similarly goddess Lakshmi is the eternal consort of Lord Narayana. Similarly Goddess Uma is the eternal consort of Lord Sadashiva.
You should notice that I say "eternal". It simply means that she does not leave her Lord practically never. Even when the Lord descends into this world (remember what I said to mean avatara), his consort will follow him:
The Vishnu Purana: Book I, Chapter IX:
http://www.sacred-texts.com/hin/vp/vp044.htm
"For in like manner as the lord of the world, the god of gods, Janárddana, descends amongst mankind (in various shapes), so does his coadjutrix Śrí. Thus when Hari was born as a dwarf, the son of Adití, Lakshmí appeared from a lotus (as Padmá, or Kamalá); when he was born as Ráma, of the race of Bhrigu (or Paraśuráma), she was Dharańí; when he was Rághava (Rámachandra), she was Sítá; and when he was Krishńa, she became Rukminí. In the other descents of Vishńu, she is his associate. If he takes a celestial form, she appears as divine; if a mortal, she becomes a mortal too, transforming her own person agreeably to whatever character it pleases Vishńu to put on."
Now, you should understand something. In Re: LORd SIVA : A Gaudiya Vaisnava Perspective I have already explained that all forms of Lord Krishna are actually his amsa or parts and thus His manifestations or expansions. Gaudiya Vaishnavas explained, and thus the scriptures say, that all these Goddesses are actually expansions of Sri Radha who is the original Goddess just like Lord Krishna is the source of all forms of Lord Vishnu and as such the original Lord.
Regarding Bhagavad Gita 15.7
Individual living entity or jiva is said to be an amsa or particle of the Lord.
There is a difference between amsas that are Lord Vishnu and those that are jivas. Amsas that are Lord Vishnu are usually especially powerful. Jivas are also amsas of the Lord but with a relatively small power.
Amsas that are jivas are called vibhinnamsa "separated parts" because they are not the Lord Himself. Jiva is not Lord Vishnu, but is subordinate to Him.
Amsas that are Lord Vishnu are called svamsa or "a personal expansion or personal part" of the Lord. They are Lord Vishnu Himself, personally.
It is important to know that all the amsas are eternal whether they are the Lord Himself or not the Lord Himself but the jivas.
Even when jiva attain liberation it will continue to exist as jiva because it is described in Bhagavad Gita 15.7 as sanatana or eternal.
regards
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