Sorry, those don't sound natural to me (I'm a native speaker). If I understand your dialog correctly, something people might say jokingly in this situation is the saying "Great minds think alike!" You can say this, for example, when you and a friend surprise each other by both having the same idea at the same time. Hope that helps.

I would put forward that in this particular sentence the correct term is “like-minded as we are”. You are stating a similarity. To use the second expression you would be comparing a similarity between a group to another person or group of people. “Italians are very expressive when they speak as are we, the French”

'As are we' means 'we are also going to do that same thing/we are going too'. As we are doesn't really mean anything in and of itself - you need to add something after.