As Peter said, in the first version, 'common' could have the 'many people do it' sense, or it could be 'we both do it'. I think it is ambiguous rather than specifically the first. The 'shared' option makes it more likely to be 'we both do it' rather than 'we do something that a lot of people do'. It is probably therefore better to use the second version.

Hi, The two phrases have different meanings. The first refers to "common hobbies". In English this usually means hobbies commonly done. For instance, cycling is a common hobby. Having hobbies in common, on the other hand, usually means sharing an interest in similar hobbies. The word "common" can also have a derogatory meaning. Check a dictionary, if in doubt.

Yes, mostly! All of them except "We have some common hobbies" sound right. You could also say "We share some hobbies", with "common" being implied here because you're sharing the hobbies already.

Thanks