Some of my images are cut off on the right side when hyou clicck on them to reply, and when you click again you see the full image.
All the images I post have the longest side less tha n 1000 pixels.
Some othe images posted are very much larger, bujt are always shown in full.
Any idea why?
This is a known issue with the Discourse software. Just means you need to view at full size by clicking on the image.
Wasn’t like this until the last ‘upgrade’ and image fields were cropped. Like many so-called upgrades it seems that visual appearance was given priority over practicality. It’s called the washing-machine syndrome where designers move the buttons and then tell you its a new model 
Is there a max size for photos embedded in posts?
There is but the admins will know that. As always you should consider that there are users with limited bandwidth that may see too slow loading. Personally I only upload a max of 2400 pixels on the long side and no more than 75% resolution.
If you want to know the limit you can raise a support request at the main website as they should be able to give you an answer. The other option, if you want to upload high-resolution images is to use a site like IMGUR and post a link.
