more picture

Do you have any idea what the name of that plant?

They are not peonies. Peonies need 1-3 months of warm weather (Autumn ) to generate roots, then 1-3 months of cold weather (Winter) to sprout in spring.

They will not sprout in 7 days.

Hi Rafflesia. I had some peonies root from seed last year, here's what one of them looked like. I don't know what the seedlings are that came up, I'm not very good about IDing plants. There is a forum for that, though, or just keep them in pots until they're a bit bigger and more distinctive. Unless you're absolutely sure they came from the seed you were sold or given as peony though I wouldn't give up, could just be some contamination in the pot from another seed source. If the seedlings growing now end up just being weed or unwanted I'd just pluck them and wait to see if a peony emerges.

Those are definitely not peonies. Peonies have relative big (blueish) black seeds (the size of a big pea) and take a long time to germinate. If you sow them now most of them will germinate in the spring of 2016, some might germinate even a year later (2017). That is when you got fresh seeds. 'Old' peony seeds come into a state of deep dormancy and its difficult to get these germinated.

It looks like you've been fooled or that the vendor has made an honest mistake. I won't speculate and keep my thoughts to myself ...

When buying peony seed always buy from reliable sources. When someone advertises with heavily photoshopped pictures for me that is usually a sign not to buy there. When somebody offers peony seed out of season: don't buy it.

These flowers look like Petunias

I thought so too Simona...