Thanks again for doing all this; sorry for not having had more to say!
First, the Hawaiian part. All your cousins and siblings are either kakak older sibling/cousin or adek younger sibling/cousin. If you want to specify that you only talk about your parents' childrens you can soecify this as kakak kandung or adek kandung. Note that kakak/adek is also used in compounds in a wider sense that includes friends and the like. It is also a common form of address. Sometimes the Sanskrit loans saudara 'brother, male cousin' is also used to refer to distant relatives lime cousins. The female form saudari is less common, women are sometimes also refered to as saudara. Note that the Sanskrit forms are also used as a forn of address in some political contexts.
Not really related, but tangentially this idea of having two words for 'brother' reminds me of Irish. There's only one word for brother in Irish now, but it's not the ancestral PIE term. In Old Irish,
bráthair could be any brother, male cousin, or other male kinsman. It still means 'brother' in Scottish Gaelic. But at some point in Irish it's become specialised to mean a
religious brother - a monk, a friar, or a fellow member of a society. Instead, an actual brother is now a
deartháir, literally meaning "sure/certain brother", but apparently from late Old Irish and Middle Irish actually meaning 'blood brother'. What I don't know (though I imagine someone does) is whether the blood-brother word arose just because 'brother' itself was too vague (and then the latter became specialised in its monastic sense once it was no longer needed for real relationships), or whether it arose specifically because 'brother' was being used so much in a religious context. Either way, clearly Middle Irish people felt the need to constantly be saying "no, your
actual brother", because 'brother' had become used so commonly for something else. [or more generally as the Irish moved away from traditional clan structures toward modern nuclear families].
[a very similar process occured in Ancient Greek, where the inherited word for 'brother' likewise spread out to be any male clan member, and then a co-member of a social or political grouping, while a new term, "same-womb", was adopted for actual brothers. One difference, though: in Greek this only happened with brothers, whereas in Irish it happened with both brothers and sisters]
[further tangent:
deartháir is an infuriating/ridiculous word, because it's not pronounced as spelled. In fact, Wiktionary lists six different pronunciations, NONE of which match the spelling. (instead they match five different wrong spellings, with various forms of irregular metathesis and length changes). Ah, Irish.]
Similarly, your mothers sister and your mother are all referred to as mama. And your father and his brother are all referred to as bapak. But here's the catch and this is where things start getting Iroquois. Your mother's brother is your om and your father's sister is your tante. Both terms are derived from Dutch and cannot be specified any further. Mama and bapak can however indicate relative age. Your mother's younger sister is your mama adek or madek for short. Similarly, your mother's older sister is your mama tua. Bapak adek ~ padek and bapak tua are used in the same way for your father's brother. Note that om and tante are also used by children and young adults to adress people from their parents generation that they don't know very closely. Madek and the like cannot be used in that function. Mama and bapak are common terms for adult men and women respectively and also used as a term of adress similar to Emglish Madam/Sir/Mister/Miss(es). For women, the Standard Indonesian form ibu is sometimes used, for men the forms are identical anyway.
Another tangent, I'm afraid: I wonder whether there are any languages that have different words for "aunt younger than ego" and "aunt older than ego" (and equivalently with uncles)? After all, in large clans, and particularly with polygamy, the situation of having members of one 'generation' be younger than those of the 'next' generation must not-infrequently arise...
Children are generally referred to as anak, independent of gender and age. Your siblings' children (i.e. nieces and nephews) are also referred to as anak. Again, biological parenthood can be indicated by adding kandung, i.e. anak kandung. In many regions, additional terns are loaned from local languages that specify more information, e.g. on gender and birth order. I also heard the term keponakan used for more distantly related nieces and nephews. However, this term is also used for distantly related cousins.
Is
kandung as ungainly or rare as adding 'biological' in English? [i.e. is this a technical disambiguation method, or is it actually a common, more precise term used on a regular basis?]
Your grandparents are your nenek 'grandmother' and your kakek 'grandfather'. More basilectal forms also use the form tete 'grandfather', which is also used by children as a term of address for the christian god. Since traditional polygamy was still more common a few generations ago, I also learned the terms for your grandfather's wives that are not your grandmother. They are dependent on age/order if marriage: nenek mudah 'younger wive of your grandfather' and nenek tua 'older wive of your grandfather'. Literally they can be translated as 'young grandmother' and 'old grandmother'. Your grandchildren are referred to as cucu, again independent of age and gender.
Step-parents are generally stigmatized. The terminology can be derived by adding tiri after the terms for parents, children and siblings. They are not usually added to more complex kinship terms. Adoption is common and not usually indicated in speech, except by contrasting it against kandung 'biological'. There is also a looser form of adoption, where children still keep their biological parents but go and live with some other family who pays for their education. This is common, especially inside larger 'clan'-like structures, and children are often terminologically integrated into their host family as well as their biological family.
I would agree that this could loosely be called 'fostering' in English, since it's what fostering traditionally was. However, you're right that I wouldn't call it "foster care", a neologism that is narrower in meaning. [for this reason I might not call it 'fostering' at all in the context of describing specifical relationships between individuals to someone unfamiliar with the local system, though I probably would call it 'fostering' in a more anthropological context, if that makes sense.] [diachronically, modern 'foster care' is essentially a euphemism for wardship, by comparing wardship to traditional fostering, that has ironically largely now overshadowed the original meaning that it was relying on for its euphemism...]
[the older sense is still sometimes found colloquially in the sense of the word "foster-father", which is often much broader than the modern technical sense of a paternal guardian in a system of foster care]
[incidentally, similar relationships, not called fostering to my knowledge, were actually common in English society in the Early Modern period (and even into the 20th century to some extent). It was not uncommon, particularly with women, for a young person to be sent to live with a relative or trusted family friend in London (and presumably to a lesser extent in other cities), for years at a time, in order to catch a husband, or at least pick up some of the education or social experience that might help them catch a local husband when she returned to the country. In the 19th and early 20th centuries, a combination of railway commuting and the rise of the respectable middle-class boarding house and landlady largely did away with the need for such procedures.
Something I just learned recently puzzled me a bit. Your cousin's grandchildren are your cucu and you are their nenek/kakek. I guess it makes sense from some perspective, but it was surprising for me at least.
This seems logical, and I was actually going to ask that question two paragraphs ago just to confirm, before I saw you say that.
If your mother and your mother's sister are both
mama, then you'd expect your grandmother and grandmother's sister to both be your
nenek. And likewise, if no distinction is made between a sibling and a cousin, then your grandmother's cousin should still be your grandmother. Relatedly: are your mother's cousins also your
mama?
And more general musing: how much of the similarity to Indo-European kin terms is influence, and how much is the coincidence of babytalk...