Adding / Updating the profile picture
At the moment, the only way for Wordpress to update an user's profile picture, is by using Gravatar. Here's the process:
Access gravatar.com, click "Create your own Gravatar" and create an account.
You'll have to go to your email to verify the account. Once you do it, go back to the Gravatar site, and it should look like the following image. Click "Add a new image"
Select the source from where you want to add the picture and add the image you want
It will give you the option to crop the image or adjust it. Once you are ready, click "Crop and save". Then select a rating (usually G)
All set! It will be reflected on your account very quickly.
Adding / Updating the name and biography
Go to the "Users" label on your admin panel, and select an user to edit. You will be able to enter their full name, select a way to display it publicly and add the biographical info.
Finally, scroll down, click "Update User" and it's all set!
Updating the author on a blog post
The easiest way to do this is by going to the "Posts" label on your admin panel, locating the post you want to update, hover over your mouse there and select "Quick edit"
Select a different author from the "Author" dropdown and hit "Update"
Note: If you don't see the "author" dropdown it might be due to a lack of other users added to the site. Users under "editor", "author" and "admin" roles can be selected here.
This is how it will look like in the blog post: