Yes, this bag has padded shoulder straps. 

The diameter of the biggest part, namely the camera head, is 23mm/0.9in. 

I have not looked for a specific travel case, but unless you are being really rough with it I would say a padded envelope or a generic small case would do it. It's pretty sturdy. I take it to to the office sometimes and just put it in one of the pockets of my laptop case. Also, for extra protection against scratches I never removed the clear plastic film that comes over the screen. Except for the red ""pull here"" tab, you can't tell it's there. 

Dear customer: This construction time-lapse camera is a waterproof and dustproof integrated design, and the rating is IP66, so you don't need to protect items such as cases. Hope our answer is helpful to you. 

I don't know the exact size but it even fits 12-13 year old kids.