No, there is no way to perform tasks on behalf of another user without logging into their account. For example, to request feedback on behalf of your Executive, you would have to access their account. 

You can schedule a 1-on-1 for someone else by inviting them and the person they will have the 1-on-1 with to a calendar event. Then they will both be notified about the meeting and can proceed to have the 1-on-1 on Fellow.