Identical websites sharing same users?

I am going to setup two identical e-commerce sites (using wordpress). The only real difference i want is the content on each site. What would be the best method of having users account information shared between sites?

To make it easier to understand ill list each major question below:
1) How to get user information shared between sites
2) How to have users stay logged in with their account between sites
3) Is it possible for sites to share other information? E.G Custom profile fields

I realise this post is pretty brief but i can elaborate more on any aspect if you ask 🙂 Thanks

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