Now that the information has been presented the questions can be answered in the light of this information.
1) Is the UN/DPI a secular (as opposed to religious) organization?
Yes
(2) According to JWs, does the UN/DPI have any objectives contrary to the Bible?
The UN/DPI objective is to disseminate information about the UN. That is the only responsibility of DPI NGOs. It could be information about what the UN has done and is trying to do. The information could also be of a critical nature. The NGO does not support the UN in all its endeavors nor is it required to only give praise to the UN as apostates would lead us to believe. The phrase within it 'own aims and purposes' is applicable to NGOs. The word support means 'furnish corroborating evidence'.
(3) According to JWs, is the UN/DPI under judgment by Jehovah God?
All governments are under judgement by God but all are God's servants that we should be in subjection to.
(4) Did the Watchtower Bible and Tract Society of New York, Inc. become part of the the UN/DPI?
NO The WTS was not incorporated into the UN. Oleg agreed.
(5) According to JWs, is the UN/DPI approved or diapproved by God?
All governments and their agencies are God's public servants so in one sense they are approved by God to carry out their God given authority. They are disapproved because they do not submit to God's kingdom.
(6) According to JWs, are any of the the other members of the UN/DPI disapproved by God?
I am sure that some are but not for being an NGO with the UN/DPI. I am not sure that all NGOs with the UN/DPI are disapproved by God.
Your questions are too broad and general. If you want to ask more specific questions then More details can be provided on the above answers if necessary. I believe I have answered all the above questions already in a more specific way by the material I have presented.