Can I send photos in Messenger?

Yes you can!

If you would like to send a photo to a member from your device without uploading it to your gallery you can do this by clicking on the photo icon at the bottom of the text box in Messenger:
 

Click browse: 
 

Select the image you want to send to the member:
 

Click the 'Send Photo' button and the photo will be sent directly to the member: