Machin's teeth are bloody when he is first tied up. However, when Speedy comes to talk to him alone, his teeth are no longer bloody.
When Oliver first enters Felicity's hospital room she is looking to her left and there are red flowers on the table to her right. Later on Oliver and Laurell are talking in front of a large window and Felicity is facing towards them, towards her left with the red flowers behind her right shoulder and the door to the room clearly visible on her right side, opposite how Oliver originally entered the room.
Since they know that Ray is alive, and because he cares very much for Felicity, there is zero reason they choose not to use the nanites to help save her life during surgery and stabilize/repair her spinal column. (Like they did with Ray's blood clot)