High Valyrian Declining
General Question about declining that I have got from reading the wiki or the duolingo lessons. When declining do you decline the whole sentence or just that particular word? For instance, I made a friend a birthday to say Happy Name Day in HV "Biarior Brozio Tubio". Is it right to decline brozi and tubis or do you just decline brozi? Did biarior need to be declined into the genitive as as well?
When declining you decline the noun, and also you decline any adjectives to "agree in gender, case and number ... with the noun they modify."
The sentence can have multiple nouns, and each noun is allowed to be in whichever of the cases is appropriate for its role in the sentence. There are examples of the cases on the wiki.
My belief on what you were trying to write is that you should have Tubis Biare for "Happy Day", and that "Name" should have the genitive, which would have given the sentence: Brōzio Tubis Biare! However, I would much prefer that a course moderator or even David J Peterson give the final word on this, or another construction to use for "Happy Birthday".
Incidentally: Kepo Tubis Biare — Happy Father's Day can be found in the wiki vocabulary. Try searching in the page for it (ctrl+f works on some computers. I think iOS may use a different shortcut.)
I am hoping what I have written is a) accurate, and b) not misleading. I must add the disclaimer I am not connected with the course or the course contributors - what I have written here is only my opinion about what you have asked and the example you have given.
Yeah I wish information regarding declining nouns and having nouns and adjectives agree was more clear than it is right now. Or at least easier for beginners to get a grasp of what is needed to make a grammatically correct sentence.
Happy New Year - Biaror Arlior Jēdari, is two adjectives modifying a noun. Both adjectives (biare and arlie) are declined to be nominative or accusative (no difference in declination), class II and III respectively. The noun (jedar) is declined to be accusative singular as if it was "dependent on an unstated verb". Could also be nominative plural though. Not much more information is given on this particular sentence. EDIT: Biaror and arlior are also declined to be Terrestrial/Aquatic, as jēdar is an Aquatic noun.
Happy Fathers Day - Kepo Tubis Biare; Kepo (n.)(Lunar) being declined to be dative, tubis (n.)(Solar) and biare (adj.)(Lunar?/Solar?) are in the nominative or accusative cases with no declination. I personally would have thought to put the adjective (biare) at the beginning, and would have declined kepa to be either plural or collective. Although my understanding of the grammar may not be 100% spot on.
To answer the original question, I believe "Biarior" (Biare; adj. Lunar/Solar) should be "Biaror" (due to the example of Happy New Year). Brōzi (n.)(Lunar) may be in the dative case (for unclear reason) due to the Fathers Day example (to become brōziot). Tubis would probably not be declined though. So I'd've said "Biaror Brōziot Tubis".
Sorry for the wishy-washy accuracy of my comment; it's difficult for me to understand what is going on, so I did my best. :)
As a verb to decline, in this context:
To inflect for case, number and sometimes gender.
Source: Definition 7 of https://en.wiktionary.org/wiki/decline#Verb
Informally, all this means is that depending on what role the noun has in the sentence, its ending will change. And in High Valyrian also the ending of the adjective will change to agree with the noun.
With luck and persistence you will gradually learn how they change as you progress through the course; this remark can stand for Irish as well, which I see you are learning. Sometimes I find it also helps to locate an article or wiki-page on some aspect of grammar like this, but this is probably best done when you have something specific you want to look up.
I wrote a post about this on reddit: https://www.reddit.com/r/HighValyrian/comments/8l3w0u/a_quick_review_of_the_basics/
This might be overly general for you because it only applies to the nominative and accusative cases (the first section of the Duolingo course), but if you're not really sure about which words in the sentence decline then it might be a good place to start.
The broad answer to your question is that all nouns and adjectives are declined according to case as well as number and gender, but certain ones decline more, others less, depending primarily on their theme vowel or class.
In a phrase like "happy name day" you would decline all three words appropriately, but there are some questions about usage that need to be cleared up, like which case(s) we're supposed to use, and whether the words you chose are appropriate. (For example, can a day be happy? Do days have feelings? Or is HV like our language where things that make us happy can be described as happy ourselves.)
I don't know what cases HV uses for this, but I can think of a couple possibilities based on languages I know. One possibility is to use the accusative case, which you see in languages like Esperanto. "Happy birthday!" is understood as being short for the sentence, "I wish you a happy birthday!", hence the accusative. In a language like Russian, the instrumental case is used, and the phrase is essentially "With birthday!"
For HV, the closest examples given seem to be in the nominative case, which might also work depending on the language, maybe as a fragment of the phrase, "May the birthday be happy."
PS. I believe the other posters are right to put "name" in the genitive case, as this seems like a very obvious thing to do. "Name day" = "day of name". I mean, there may be a remote possibility that someone would want to use an adjectival form of "name", but genetive seems easier/better.