You have a very serious issue; criminal sexual conduct involving a minor is a very serious matter for immigration. The fact that your criminal case is resolved is totally different from what will happen in immigration. Best advise: take all your documents to an experienced immigration attorney to review your options. If you are in custody, you should make an arrangement for the attorney to get the documents for review and then meet to discuss.
You are going to be in removal proceedings. You need to hire an experienced attorney to review your documents and see the best way to avoid removal. Make sure to notify the USCIS of your address if you move because your removal documents will be mailed to the last address they have.
You cannot transfer the petition to new organization; you will need to re-file under the new entity. Make sure the new entity meets all the requirements for R-1 petitioner and you are in valid status when you refile.
With a valid greencard, no criminal issue and your Cambodian passport, you shouldn't have any problem traveling to your country. The issue is that your card is too old and need to be renewed. You should explore the renewal first before traveling to avoid issues at reentry. It does not appear that you need a re-entry permit, but you will need to discuss your situation with an experienced immigration attorney to make sure all issues are covered.
Unfortunately, the answer to your questions depends on a lot of situation. If your Adjustment of Status application is still pending, you may be able to renew your EAD. But an experienced immigration attorney can review the situation to make sure there are no other issues that will prevent the approval of your EAD application.
The question is not quite clear: rejected or denied or closed? It will be worth your effort to take all the documents to an experienced immigration attorney. Only will you know exactly the best way to handle your situation.