Is god Aryaman present in post-vedic texts?
Yes the god Aryaman is present in Post-Vedic texts like puranas also.
The Brahma Purana lists him in twelve Adityas and describe the sun in the form of Wind as Aryama -
As Aryama he is the wind.
In each month of the year its is different Aditya ( sun who shines.)
Aryama in Vaishakha.
Its said in Bhagvat Purana that in Hiraṇmaya-varṣa Aryama worships Lord vishnu along with other residents.
हिरण्मयेऽपि भगवान्निवसति कूर्मतनुं बिभ्राणस्तस्य तत्प्रियतमां |
तनुमर्यमा सह वर्षपुरुषैः पितृगणाधिपतिरुपधावति मन्त्रमिमं चानुजपति ||
hiraṇmaye ’pi bhagavān nivasati kūrma-tanuṁ bibhrāṇas tasya tat
tanum aryamā saha varṣa-puruṣaiḥ pitṛ-gaṇādhipatir
upadhāvati mantram imaṁ cānujapati.
Śukadeva Gosvāmī continued: In Hiraṇmaya-varṣa, the Supreme Lord,
Viṣṇu, lives in the form of a tortoise [kūrma-śarīra]. This most
dear and beautiful form is always worshiped there in devotional
service by Aryamā, the chief resident of Hiraṇmaya-varṣa, along with
the other inhabitants of that land. They chant the following
It also said in the same Purana that Aryama is predominating deity of that planet Pitṛloka
वत्सेन पितरोऽर्यम्णा कव्यं क्षीरमधुक्षत ।
श्रद्धया श्राद्धदेवताः ॥14.18. 8॥
vatsena pitaro 'ryamṇā kavyaḿ kṣīram adhukṣata
mahā-bhāgāḥ śraddhayā śrāddha-devatāḥ
The fortunate inhabitants of Pitrloka, who preside over the funeral
ceremonies, made Aryama into a calf. With great faith they milked
kavya, food offered to the ancestors, into an unbaked earthen pot.
Footnote - Those who are interested in family welfare are called pitṛ-vratāḥ. There is a planet called Pitṛloka, and the predominating
deity of that planet is called Aryamā.SB 4.18.18
Discribe the connection of aryaman with milkyway?
The answer of this is already present here. You can read it in this answer of mine
What are the verses revealing Aryaman?
Here are some of the verses revealing Aryaman. He is not praised separately or independently in vedas but often with Mitra and Varuna.
नु मित्रो वरुणो अर्यमा नत्स्मने तोकाय वरिवो दधन्तु |
विश्वा सुपथानि सन्तु यूयं पात स्वस्तिम्भि : सदा न || 7.63.6 ||
Now Mitra, Varuṇa, Aryaman vouchsafe us freedom and room, for us and
for our children. May we find paths all fair and good to travel.
Preserve us evermore, ye Gods, with blessings. RV 7.63.6
Ralph T.H. Griffith and here is Hindi Hindi translation.
वि ये दधु: शरदं मासमाद्हर्यज्ञमक्तुं चाद्रुचमम् |
मित्रो अर्यमा क्षत्रं राजान आशत ||RV 7.66.11||
They who have stablished year and month and then the day, night, sacrifice and holy verse, Varuṇa, Mitra, Aryarnan, the Kings, have won
dominion which none else may gain. RV 7.66.11 Ralph T.H.
Griffith and here is Hindi translation.
Here are some of the additional mantras of Aryama from Rig-Veda.
The Rig-Vedic verses Praising Aryama with Mitra-Varuna for welfare of self with rest of family members.
It says let our progny get the good wealth ,let our path of progress be easy. Let we and our family be well nourished by the grace of Aryama.