Yes. They tried to keep him contained, but he broke out after succumbing to the virus. Barnes delivered the kill shot.

[He catches the movement, Coulson's eyes closing and for Coulson it's a huge tell. He's not used to that.]

Me too. I...I asked Adele to kill me, if it came to that, although Stark wasn't having any of it.

[And then they'd had to put those plans into practice with Steve instead. He's silent for a moment before answering.]

The Malnosso were going to bomb the compound. Thankfully the medical teams managed to find a cure before that.

As for the rest... it's not my place to tell. Ask Stark, if he wants to tell you.