Priority date of US patent for filing in other countries?

• In general, priority date is the date of filing of the first patent application (either provisional or non-provisional). Paris Convention, an international patent treaty, allows the owner of U.S. patent application to file patent applications in other countries (which are Paris Convention member countries) within one year from the U.S. filing date. The U.S. filing date serves/acts as the priority date for the foreign patent applications.

Does 12 months from 16 June 2017 mean priority can be claimed till 15th June 2018 or 16th June 2018?

18th June 2018. Exactly 1 year, latest on the day having the same date 1 year later extending to the next working day. And 16th and 17th were weekend days. (It's like that in all jurisdictions afaik, but I can't promise).

You can check the priority, it is marked on the cover page. A priority has to be explicitly claimed so the date alone doesn't tell you anything. Claiming priority later than 12 months can be possible in some jurisdictions if the date was missed on accident for example.