Part of. The Order Service, as stated in the post you quote from, was ordered to help in the roundups of Jews taken to Chelmno and later to Auschwitz. Yes, part of.
Care to explain how that works? If the Germans wished to exterminate the Jews, why permit than to have they own bank system? Postal office? Workshops?
Lodz was exceptional in being the longest-lasting ghetto and for its extensive workshops supplying the German military and industry; it was not, for example, part of the General Gouvernement where Aktion Reinhard was organized and carried out - but even in the GG some Jews were kept alive for forced labor, as you would be aware had you checked this thread as you were advised to do. Lodz itself was maintained as a working ghetto until its final liquidation. Still, approximately 70,000 Jews were deported from Lodz to Chelmno for execution in gas vans at the death camp in Kolo County during 1942; these were mostly ghetto inmates deemed by the occupying German authorities not to be capable of work and thus not worth keeping alive.
The Jews were not supposed to starve to death?
This question doesn't make any sense. I can say that in Lodz ghetto starvation and diseases related to malnutrition were rampant, and thus mortality was significantly higher than normal. However, at the same time, the authorities there wanted to keep Jews alive and productive. On occasion, observing that Jewish inmates would pass out at work in extreme cases or were lethargic and unproductive from malnourishment, Biebow's Ghettoverwaltung increased rations - minimally, for the purpose of maintaining labor productivity. A memo written by Rolf-Heinz Hoppner to Eichmann on 16 July 1941 expressed the situation thus: "There is an impression that District President Ubelhor does not wish to see the ghetto in Lodz disappear since he seems to profit quite well from it."
This shouldn't be hard to understand - Greiser's policy in the Warthegau was to clear out and murder much of the outlying population, to concentrate a Jewish workforce in Lodz ghetto held there by force and kept in poverty to produce economically useful goods, and finally to murder Lodz Jews judged incapable of work. In fact, Ubelhor's September 1939 confidential memo on the "Establishment of a Ghetto in the City of Lodz" explained the plan for the Lodz ghetto at the outset, "It is obvious that the establishment of the ghetto is only a transitional measure. I reserve for myself the decision as to when and how the city of Lodz will be cleansed of Jews. In any case, the final aim must be to burn out entirely this pestilent abscess." At that time, in 1939, the mass murder of Lodz's Jews was not being planned. Eventually, however, in 1942 those not able to render productive service to the occupying Germans were murdered en masse and finally, in 1944, all the remaining Lodz Jews were "burnt out" - as nearly all Lodz Jews left in the ghetto in summer 1944 were shipped for death to either Chelmno or Birkenau at that time - about 55,000 being sent to death camps and only 1400 kept alive for various labor assignments.
Are you speaking with a mirror?
I see you are neither knowledgeable nor clever; you compensate for this by being repetitive. It is a poor tradeoff, IMHO.