I agree with both points. The only gotcha with liking the photo before drilling into it, has to do with the fact the their API returns a truncated result of all the likes on the media when using any endpoint other than /media/{id)/likes.
The reason that's a problem, is that there's no way for me to know for sure if you already liked something or not. I could A) Assume most people are only clicking on the heart to like something and not to unlike something they already liked, or B) Make a request to /media/{id}/likes for every image on the page. Given the two, I think it'd be safe to assume they just want to like something.
Leaving a comment should be pretty simple ;)