I would appreciate if you could leave a review for this theme on WordPress theme repository: http://wordpress.org/themes/travelify
Yes, update will overwrite all your customizations done in the code but all settings done via Theme Options will still be there.
It is always better to make all these changes via Child Theme. In the best case scenario you would have to copy only changes values to style.css of your Child Theme. Since you did all changes right in the original file it might be difficult to move to Child Theme.
There is nothing much new in the 1.3.7, so you can skip that but I am now working on 1.4 which will be a must have update for everyone.