Is there any (open) standard for importing/exporting contact from/to any mobile phone? Is there any open format for importing and exporting from/to any mobile phone. It doesn't have to be a smartphone, it could be a basic mobile phone. If any such thing exist, does is also support import/export from/to SIM as well?

Contacts is one feature which is universal in all phones so I am hoping this is some standard/format which could be used for doing this. In smartphone, it could be done by apps but what about the basic phones.

Any help/insight on this would be highly appreciated.
That format most likely is VCard (Versitcard), which even has its own mimetype (text/vcard). According to the linked Wikipedia page, it became a standard around 1996 (and since it was proposed 1995 for the first time, older devices won't know it).

Android's contacts app uses this format when directly exporting your contacts from it. To my knowledge, this format is also used when transferring contacts via Bluetooth (even to/with older devices not necessarily running Android or being "smart phones"). Mail clients support it as well. So if you're looking for any standard here, this most likely is it.