Is there any difference between financed direct by NIH or indirectly financed by NIH (hired by a professor) for J1 waiver?
-Of course, no. If NIH can waiver their own J-1 employee funded by NIH, there is not reason the J1 holders in other institutions (funded by NIH) can not get the J1 waiver.
If denied, do you think I can appeal?
-No if your J1 waiver is based on "No objection".