Q:

Nirvana is the ground layer underneath them all

According to this answer:

Nirvana is the ground layer ("dhatu") underneath them all. ... 
Nirvana is this most fundamental law (the formula, the rule, the
  program) according to which the Universe develops. 

This comment also seems to support that idea:

... the expression "the unmade is a foundation for phenomena" is
  probably an agreeable thing to say given than it occurs in the pali
  discourses "amatogadha" meaning deathless as foundation or deathless
  as ground.  There is also a reasonable way to defend it, which makes it
  not a real point of controversy imo but a rather reasonable assumption
  in that the pali wording is to be taken at facevalue and read
  literally. 

This sounds very similar to Advaita which describes Brahman as the substratum or foundation of all phenomena, just as different kinds of pots and plates made of clay, all have clay as their foundation. 
Questions:

Does the notion "Nirvana is the ground layer" come from Mahayana?  From which Mahayana subschool or text? 
Does the Pali Canon support the notion that "Nirvana is the ground layer"?  Does this relate to "amatogadha" some how?  What's that? 
The ground layer concept sounds similar to luminous mind.  However, we know that Nirvana is unconditioned, while the luminous mind is conditioned.  Does this "Nirvana is the ground layer" concept connect to the luminous mind in any way? 

A:

1.  Does the notion "Nirvana is the ground layer" come from Mahayana?  From which Mahayana subschool or text? 
Yes.  Well, they don't call it "Nirvana" - because they think this word got spoiled by abuse and acquired a dualistic meaning (as the opposite of Samsara).  Instead, they simply call it "The Ground of All", "The Absolute", "The Unity of Relative and Absolute" etc. 
This is certainly a well-known feature of Tibetan Buddhist lineages in Karma Kagyu and Nyungma schools that adhere to the so-called Shentong interpretation of Emptiness: 

https://en.wikipedia.org/wiki/Ground_(Dzogchen)
https://en.wikipedia.org/wiki/Rangtong-Shentong

Shentong was systematized and articulated under that name by Dolpopa Sherab Gyaltsen (1292–1361), who identified absolute reality with the Buddha-nature. 

...  

The earliest shentong views are usually asserted to have been presented in a group of treatises variously attributed jointly to Asanga and Maitreyanātha, especially in the treatise known as the Unsurpassed Continuum (Uttaratantraśāstra, also called the Ratnagotravibhāga),[22] and in a body of Mādhyamaka treatises attributed to Nāgārjuna (e.g., the Dharmadhātustava, "In praise of the Dharmadhatu"). 

...  

Rigpa has two aspects, namely kadag and lhun grub.  Kadag means "purity" or specifically "primordial purity".  Lhun grub in Tibetan normally implies automatic, self-caused or spontaneous actions or processes.  As quality of rigpa it means "spontaneous presence".  It may also mean "having a self-contained origin", being primordially Existent, without an origin, self-existent. 

...  

Buddha-nature is immaculate.  It is profound, serene, unfabricated suchness, an uncompounded expanse of luminosity; nonarising, unceasing, primordial peace, spontaneously present nirvana. 

...  

The practical training of the Dzogchen path is traditionally, and most simply, described [as:] To see directly the Absolute state, the Ground of our being is the View; the way of stabilising that view, and making it an unbroken experience is Meditation; and integrating the View into our entire reality, and life, is what is meant by Action. 

In Chan and Zen schools this is generally discussed under the heading of Buddha Nature and "One's True Nature":

https://en.wikipedia.org/wiki/Buddha-nature

... the ultimate universal ground also has always been with the Buddha-Essence (Tathagatagarbha), and this essence in terms of the universal ground has been taught by the Tathagata.  The fools who do not know it, because of their habits, see even the universal ground as (having) various happiness and suffering and actions and emotional defilements.  Its nature is pure and immaculate, its qualities are as wishing-jewels; there are neither changes nor cessations.  Whoever realizes it attains Liberation

...  

This "dharma of the one mind", which is the "original tathagatagarbha", is said to be "calm and motionless" [...] The tathagatagarbha is equated with the "original edge of reality" (bhutakoti) that is beyond all distinctions - the equivalent of original enlightenment, or the essence. 

2.  Does the Pali Canon support the notion that "Nirvana is the ground layer"?  Does this relate to "amatogadha" some how?  What's that? 
I believe it does.  There are many pointers spread around Dependent Origination teachings, and all the descriptions of Nibbana, with references like amatogadha and amata-dhatu, the Buddha's story about him getting "to the end of the world" etc. 
3.  The ground layer concept sounds similar to luminous mind.  However, we know that Nirvana is unconditioned, while the luminous mind is conditioned.  Does this "Nirvana is the ground layer" concept connect to the luminous mind in any way? 
I don't know why you say "we know" that luminous mind is conditioned.  In Mahayana, the fundamental luminosity of mind is considered unconditioned (see Rigpa, Clear Light).  

https://en.wikipedia.org/wiki/Rigpa
https://en.wikipedia.org/wiki/Luminous_mind#Vajrayana

In Tibetan Buddhist Dzogchen literature, luminosity ('od gsal) is associated with an aspect of the Ground termed "spontaneous presence" (Lhun grub), meaning a presence that is uncreated and not based on anything causally extraneous to itself.  This term is often paired with 'original-purity' (ka dag), which is associated with emptiness (shunyata), and are both seen as inseparable aspects of the Ground.