Hi. The above is what the matter is about but my understanding of these grammatical matters is very limited & extremely superficial. You just need to do your best to study the dictionaries and study contextually the suttas where these words are found.
For example searching the dictionary & suttas:
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the dictionary (here SuttaCentral ) tells us upādāna is neuter noun (thus also can be used as an adjective in Pali) derived from fr. upa + ā + dā. It is a noun in SN 12.2, where it says: “What is upādānaṁ?” (singular; not plural). We can learn upādānaṁ (the neuter noun) is singular by looking up a declension table, such as on page 18, here: https://host.pariyatti.org/plc/EngPaliGrammar_w.audio.pdf It is an adjective in SN 56.11 in the word compound “pañcupādānakkhandhā”. Because it is in the middle of a word compound, no declension can be known.
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the dictionary (here SuttaCentral ) tells us upādā is an adverb; shortened ger. of upādiyati for the usual upādāya in specialised meaning. The abbreviation ‘ger.’ means ‘gerund’ (look up what it means on Google). The abbreviations used in the PTS Pali English Dictionary can be understood here: The Pali Text Society's Pali-English Dictionary The same word search gives the impression upādā is not found in any suttas but is only found in later texts. The usual “upādāya” is found in suttas, such as:
‘Reverend Ānanda, the notion “I am” occurs because of grasping, not by not grasping.
‘upādāya, āvuso ānanda, asmīti hoti, no anupādāya.
SN 22.83
A different use is below:
The four primary elements, and form derived from the four primary elements.
Cattāro ca mahābhūtā, catunnañca mahābhūtānaṁ upādāyarūpaṁ.
This is called form.
Idaṁ vuccati rūpaṁ
SN 12.2
- In Pali, the verbs generally/often end in “ati”. Therefore, above “upādiyati” appears to be a verb. So we can look this up, here SuttaCentral , where the dictionary says it is “present 3 singular”. Studying a sutta under the same word search, there is for example:
This is called a noble disciple who gets rid of things and doesn’t accumulate them;
Ayaṁ vuccati, bhikkhave, ariyasāvako apacināti, no ācināti;
who gives things up and doesn’t grasp at them;
pajahati, na upādiyati
SN 22.79
So when we read the suttas, we come across these different terms such as:
When someone lays down this body and takes up another body, I call them ‘blameworthy’.
Yo kho, sāriputta, imañca kāyaṁ nikkhipati aññañca kāyaṁ upādiyati tamahaṁ ‘saupavajjo’ti vadāmi.
- SN 22.48 (adjective only)
Any kind of form at all—past, future, or present; internal or external; coarse or fine; inferior or superior; far or near, which is accompanied by defilements and is prone to being grasped: this is called the aggregate of form connected with grasping.
Yaṁ kiñci, bhikkhave, rūpaṁ atītānāgatapaccuppannaṁ …pe… yaṁ dūre santike vā sāsavaṁ upādāniyaṁ, ayaṁ vuccati rūpupādānakkhandho.
upādāniya
adjective
- (from upādāna) likely to be taken as one’s own, tending to produce grasping; serving as a support or fuel
PTS Pali English Dictionary
upādāniya
adjective
belonging to or connected with upādāna
fr. upādāna, for *upādānika → ˚aka
We can probably confirm upādāniyaṁ above is only an adjective & not a noun because the ending “iyam” is not found the declension tables.
Yes, it seems so. 
trillion of things I must bring underneath me.
Well it’s a good attitude to take. If my daughter asked me that I’d say, “your mother.” Enjoy your soft clouds and blue sky in the middle of this good night, Stephen.