Dinah Madani works for The Department of Homeland Security (DHS). However the badge she wears is an Immigration and Customs Enforcement (ICE) badge and is clearly visible.
When Sarah Lieberman takes the turkey from the oven, she immediately removes the oven mitt and proceeds to grab the still very hot metallic temperature gauge from the turkey with her bare hand and it doesn't burn her.
Russo is able to escape from his apartment by killing the seven DHS agents sent to look for him. Russo is a former Marine Corps Force Recon operative, he is a highly skilled marksman and trained, experienced killer and he currently owns a private security company and has access to a huge arsenal of weapons. Madani is well aware of all this and of how dangerous he is so it seems extremely unlike her to only send seven regular agents to his house, knowing how dangerous and well armed he is she should of sent a fully armed tactical team.
When Dr Hamilton Madani is treating Frank's wounds he diagnoses him with a tension pneumothorax and proceeds to perform a thoracentesis sticking a needle in Frank's chest to relieve the pressure. Except blood instead of air comes through the catheter which is indicative of a hemothorax.