That leaves us, I think, with this rule: Either so (gliny) Nil or soa (gliny) selë Nil is correct.
And the genitive would be soei glinii Nilei and soe glinye selëi Nilei, respectively? That is, the adjective uses the masculine ending when used with a masculine river name (and a feminine ending when used with a feminine river name such as Svetla) but always a feminine ending if selë is explicitly stated? (But a masculine river name still declines like a masculine noun, even if selë is present, right? And it agrees with selë in case?)
So agrees with the name of the river if selë is not present. Thus: So Eärdur e beluana, ac ditavu soa selä Raum, 'the Eärdur is beautiful, but I prefer the river Rau'.
Strange; I would have expected So Eärdur e beluan, with the adjective agreeing with the name of the river (which is masculine). Your sentence looks as if beluan agrees in case with the unstated selë, but that clashes with the example given in syntax.htm: Soa sazë e guessë, er ilu e imbushäm. = The prince [f.] is powerful [f.], and he [not she] is tasty [m.]. Here, guesse is feminine, to agree with the explicit sazë = prince, not with the unstated uestu or ser. So I would expect adjectives to agree with the explicit (masculine or feminine) river name, rather than with the unstated feminine selë.
The river name does decline.
Ah, I think that answers the question "does the river name decline when selë is used". Thanks.
Foreign nouns can all be assimilated into Verdurian, and therefore all decline. You choose the declination according to the ending. (For personal names, Verdurians would manhandle the word in order to get the right gender. Names in -a can of course be either gender. ...)
And if they're masculine, they decline like esta, right? So Nicola's would be Nicole if it's a woman's name and Nicolei if a man's. (Or for a contrived case: I gave it to the two Nicolas would be Ilet donai soin dhunin Nicolain for men and Ilet donai soen dhunen Nicolen for women.) (On the other hand, in this case, a Verdurian might be tempted to fit a masculine Nicola into the mold of the already-known name Nícolo, I suppose. Similarly, masculine Andrea might turn into Andrey, I suspect. But for non-Eledhe names, Frodo's would presumably be Maurei rather than Maure.)