In light of that, I shall have a go. I am no expert - but there are plenty on WAB that are. Your first pics look like
Panaeolina foenisecii which has been around quite a bit recently and although described as "not edible", is unlikely to cause too much harm, I believe.
Your other photo is a
Coprinus sp. I won't hazard a guess as to which species but none of these is known to be too poisonous, unless taken with alcohol - so unless your dog has a drink problem, it should be safe.
All that said, I would guess that dogs, having evolved as carnivores, probably have more sense than to eat fungi - especially ones they can't readily identify
With a bit of luck someone else from the fungi forum will confirm the above too.