How to get a link to a picture
There are two ways to share a link to a picture. One uses Google Photos "Share" icon. The other uses Google+
Share a link to a single JPEG image
With this method, you can share a direct link to an image. The image needs to be located in Album Archive.
Using the Chrome browser, install this extension Google Photos Direct Link
Go to Album Archive and click an album then click an image
On the bottom middle will be a message, "Image URL copied to clipboard"
The URL will look something like this: https://lh3.googleusercontent.com/series of numbers and letters=w1000-no-tmp.jpg
This URL will not expire in 30 days because the URL is from the Album Archive rather than from Google Photos
Share a link from Google Photos
(The link will not be a direct link to a JPG)
Go to https://photos.google.com or https://photos.google.com/albums
Find a photo and select it (click the circle in the upper left corner of the photo) or click the photo
Click the "Share" icon on the top right corner (the background color depends on which method you did in the previous step)
Click "Get link"
Ctrl C (copy)
Paste the link anywhere (email, text message, website)
If you would like the ability to share direct links to JPEGs from Google Photos, let Google know via their Feedback button: https://support.google.com/photos/answer/6156065