on conversation page: the left avatar should be of the username whom we are having the conversation with, instead of who started it. For example if you start a conversation and you replied last to the conversation then it will show your avatar on both side, and without clicking on it you would not know who are you having this conversation with.
Take a look at this screenshot:
The one in the red box, I would know whom I having this conversation with until I click on it.
I think its better if we have participants avatar or username on this page, so we know the participants of the convo before click on it.