Woouuuu, nice thread! But I see that some corrections are needed.
Let's start with second sentence:
English: It's good to hunt before you are hungry
Proposed Na'vi versions: Taron nìltsan leiu sre'ohakx 'efu. / Tìtaron lu sìltsan sre ngal 'efu ohakxit.
"you are hungry" translates as Nga 'efu ohakx - notice no case ending. Why? ohakx is adjective, so it can't take case ending, and therefore nor subject can.
IMO best way to say this is "You should hunt before you feel hunger" => Sweylu txo nga tivaron srekrr 'efu ohakx.
First one:
English: When the trees fall, the prolemurises will run
Na'vi: Peyhrr ayutral zivup, aysyaksyuk tayul.
I'd say: Krr a ayutral z(er)up, aysyaksyuk t(er)ul.
<er> infix is not needed and I don't see reason for subjunctive and future. Pehrr is not good here, it is questionable word. Krr a is also "when", but non-questionable. Also if you want to ask in plural (what times), use payhrr (comes from pe+ ay+ krr)
And last one:
English: Do not use a spear to remove a hellfire wasp from your friend's forehead.
Na'vi: Rä'ä s<er>ar tukru 'aku ayzize' ftu ngeyä 'eylanä 're'o. / Rä'ä sar tukruti fpi 'aku zize'ti krr a pumìl tok mì re'o a ngeyä 'eylan.
I think Puvomun is on the better way, but it can be said simpler:
Rä'ä sar tukruti krr a new 'ivaku zize'ti a mì hey ngeyä 'eylanä (Do not use spear when you want to remove hellfire wasp (which is) in friend's face (mì causes lenition on key))
or
Rä'ä sar tukruti fte 'ivaku zize'ti a mì hey ngeyä 'eylanä (Do not use spear in order to remove hellfire wasp in friend's face)
or
Rä'ä 'aku zize'ti a tok keyit ngeyä 'eylanä fa tukru (Do not remove hellfire wasp in friend's face by spear)