There is a huge amount of information already in this forum.
You can't fly direct JFK-TLV or TLV-HKG on any OneWorld tickets so you would need to go through LHR each time.
Other than that it would be a valid DONE4 ticket. You don't need a TA. Either book it online at the OneWorld website (
http://www.oneworld.com) or through the AA RTW desk (1-800-247-3247).
It would be US$9100 + taxes & fuel fines.