How to show picture of the user who triggered the rule for message activity?
Since you are using Rules to create your messages to be delivered, you can try to make the missing tokens available by using the Replacement patterns for each message type. Refer to the answer to What's the purpose of "Replacement tokens" of a Message type? for way more details on that (it explains how these Replacement tokens can be used to pass data available in Rules to the Message module).

With that, your only remaining challenge is to get access to the user picture in a custom rule. In D8 that picture has become a field also, but that's not the case in D7. Therefor you may get it to work in D7 also if you also use the user picture field module (which doesn't have an official D7 release yet, but about 11K reported installs sounds like it's a pretty stable module).