Is diem developing a standard for Diem's smart contracts ? ERC-20 for Diem?

Wondering if you have established something similar to ERC-20 for Move.

Yes–in Diem, we have the DIP20 standard for currencies.

It’s worth noting that the mechanism for implementing custom currencies is somewhat different than ERC20 because of differences between Move and the EVM; Traits or type-specific implementation in Move - #2 by sam explains in more detail.

Thanks for the response.

And do you think something similar to ERC-721 is possible too ?

Yes. There is no equivalent Diem standard yet, but this is definitely possible–see [Feature Request] Diem MOVE Standard for Non Fungible Tokens (NFTs), e.g.- ERC721 · Issue #7957 · diem/diem · GitHub for some discussion.