If I use the online booking tool will it let me book the trip starting from tlv with the same price as if I would buy the ticket from Israel (6 200 usd + taxes)? I´m not living in Israel.
Yes.
Would the ticketing airline be Malev in this case?
Apparently yes - see below for the the Q&A response from Oneworld
Question: Who is my ticketing airline?
Answer: The ticketing airline will be indicated in your Confirmation page. In most cases, it will be the airline whose code is on the first flight of your itinerary.
AA=American Airlines, AY=Finnair, BA=British Airways, CX=Cathay Pacific Airways, I6=MexicanaLink (ticketed by Mexicana), IB=Iberia, JC=JAL Express (ticketed by Qantas), JL=JAL (ticketed by Qantas), JO=JALways (ticketed by Qantas), LA=LAN, LP=LanPeru (ticketed by LAN), KA=Dragonair (ticketed by Cathay Pacific), MA=Malév, MX=Mexicana, NU=Japan Transocean Air (ticketed by Qantas), QA=MexicanaClick (ticketed by Mexicana), QF=Qantas Airways, RJ=Royal Jordanian (ticketed by American Airlines), XL=LanEcuador (ticketed by LAN), 4M=LanArgentina (ticketed by LAN)
I know or at least hope this is a valid ticket as Mileage monkey and the oneworld booking system validates it?
Seems fine.
As I can not book the right dates for the last part of the trip with the online tool I would need to use dummy dates for the last trip. Could I just inform the ticketing airline to change the dates or would I need to pay them to do so (I think not)? Would there be any problems with the date changes if I would do them in lets say December/January and my dates would be flexible?
Yes, date changes are fine (if there's availability) and are supposed to be free. However several airlines are now adding service charges for such changes; no idea about Malev. Theoretically any member airline could make the change - I'd contact AY before trying to find someone at MA who knows the product.
Is there any difference on booking the hel-xjfk-lax compered to hel-lax (as there is no straight flight I would need to enter the route so to the online tool as it will not offer me hel-jfk-lax but a connection in Europe where I can not stop because of the 4 stop limit in Europe)? Meaning if I would miss my connection in jfk would I still be able to demand the flying airline to reroute me to a later flight etc. So is the DONE3 ticket looked as one ticket regardless of how you make the routing?
In practice I think more troubles with the tool have been reported when one lets the robot make your routing choices.
I would not be using the last segment from lhr to tlv as I would fly home from lhr. Would this get me in any kind of troubles?
Theoretically yes but no reports have been lodged of any grief on that front.