Several questions 
Several answers!
Do we have examples of fì- and tsa- with dual and trial nouns? Is there any contraction? "these two trees": fìmeutral or fmeutral?
Yes, and there is no contraction:
fìmeutral and
fìpxeutral are correct.
How do we use adjectives without a noun, like in english "I make a new one". Do we use pum?
Yes, that is exactly the use case of
pum. Made up example:
Skolänga'a Tsyeykìl tskoti oeyä, tafral oel ngop pumit amip.Jake destroyed my bow, so I make a new one.Just like in English
pum / "one" needs to refer back to some other noun (in this example,
tsko "bow").
You can also use
pum with
fì- and
tsa-:
Fìtsko lu apxa, tsapum lu hì'i.This bow is large, that one is small.... and with genitives:
Tsko oeyä lu ean, pum Tsyeykä lu tun.My bow is blue/green, Jake's one is red/orange.in the Na'vi article of Wikibooks it says that expressions like "how many" takes a plural, because we dont know the number. Do we have a canonical reference or rule for it? One official example seems to contradict it: polpxaya zìsìt (not ayzìsìt)
Hmm. There is a general rule that plural gets expressed only once. In other words, if you pair a noun with
pxay "many" you put the noun in the singular, not in the plural, because the word "many" already indicates how many there are. With
polpxay I don't see why it would be different: that also indicates how many there are, so singular would be correct (IMO).
Also, I know that we use words like "below", "over" etc as prepositions, but how can we use them as adverbs? How to say "go down" or "look above" or "I am inside"?
There are separate adverbs and verbs for those:
kllkä "go down" (from
kllte + kä "ground + go"),
nefä "up, above" (from
ne + fäpa "to + top"),
mìfa "inside". You cannot just use adpositions like
äo,
io and
nemfa without a noun.
Finally, I saw recently that you use the adverbial prefix nì- as a "locative" case. Something like nìtsray = in a city. Again, do we have canonical references? I admit it reminds me a bit of Esperanto, where nouns are converted to adverbs to show location or intrument. 
AFAIK this is illegal;
nì- is not productive for nouns. Maybe you mean the adposition
mì "in" instead? For example
mì sray "in the village" (from
mì tsray, but
mì causes lenition on the next word).