The Tips & Notes list "eich ... chi" as being a possessive phrase, but is it also used to indicate a direct object? Is this used with other possessives, eg. Dw i'n dy nabod di, Dych chi'n fy nabod i, etc.?
Yes. The possessive pronouns are used with a noun to indicate possession e.g. eich afal chi (your apple); fy nghar i (my car); and also with verb-nouns to indicate the direct object e.g. eich nabod chi (know you); fy ngweld i (see me).
Ok, this one had me totally confused the first time I got it (just then). As new words it translated to 'I am yours knows you' when I hovered over the words individually and offered the only complete sensible sentence on 'chi' with 'Where are you'. So of course I got this one wrong straight up. I thought it was a translation problem at first, and I suppose it still is, but one that falls on my part, as an ignorant monolinguistical English speaker, rather than the course. :-)
In English when we say know + you, we simply stick them together. In Welsh it's slightly different: nabod + chi gives us eich nabod chi. It means the same but is formed in a different way. Hence:
helpu + chi = eich helpu chi (help you, lit. "your helping")
clywed + ti = dy glywed di (hear you, lit. "your hearing")
bwrw + fe = ei fwrw e (hit you, lit. "his hitting")
gweld + fi = fy ngweld i (see you, lit. "my seeing")
If it helps in colloquial or informal Welsh, you can drop the first word and form it like English: just helpu chi, clywed ti, bwrw fe, gweld fi and so on. So whatever you do, you're never wrong, just more informal. Dal ati / Keep it up!
So, to be sure I have this right: colloquially, the first part (e.g. eich) can be left out ("Dw i'n nabod chi"), just as with the possessive form. Is it also correct, that one cannot omit the second part and keep the first (e.g. * " Dw i'n eich nabod")?
Also, how "formal" is the written form using both parts (e.g. Dw i'n eich nabod chi.")? Would it sound strange to use that in conversation? Would it be expected in a letter to a friend? A letter to the editor in a newspaper? In a novel?
Yes that's right:
more formal: Dw i'n eich nabod
neutral (-ish): Dw i'n eich nabod chi
less formal: Dw i'n nabod chi
It's difficult to give precise rules as to when and where each are acceptable.
For starters, this is because there are so many possible situations to find yourself in. I guess the second and more probably the third are common in conversation. I don't write letters to friends really but again, texts and such follow conversational norms mostly too. Letters to editors and novels usually require more formal language.
But the second reason it's difficult to be precise here is that there are other words in the sentence too. As well as eich...chi, the form Dw i'n also has more formal and informal versions, and there's a more formal version of nabod too! Individual elements in a sentence don't work in isolation. So you might not see Dw i'n eich nabod in a formal situation much, but may see e.g. Rwy'n eich adnabod, which means the same thing.
Apologies if that's a little overwhelming, but the point I'm trying to make is that Duolingo is only a course for beginners where you're starting to familiarise yourself with the very basics of the language. Once you have these basics down pat, then you can start to branch out and learn about register, dialect, situational specific language and such. Nevertheless, ask away and I'll help if I can. Pob hwyl!
Diolch yn fawr for your detailed response. I am relishing the complexities of this ancient and multi-faceted language even as I struggle with my beginner's frustration at that very same complexity. For now, I'm just focusing on producing grammatical sentences and being able to understand the audio in real time.