Hi,
The question of PF/Pension contribution payment does not arise as the employee is on unpaid leave, and hence no contribution needs to be paid to the PF account. The term medical insurance you are referring to is Mediclaim insurance, I believe (which is offered by the company). Mediclaim insurance can be used in India only. For international travel, the employee needs to take an overseas Mediclaim policy separately.
If the employee is on a trip abroad for personal reasons, there is no need for the company to provide overseas Mediclaim for the employee. However, if the employer is deputing the employee abroad, then it is the responsibility of the employer to organize a Mediclaim policy along with travel and boarding arrangements.
Normally, employers will not permit employees to go on long leave (even without pay) for higher studies during their employment unless there are specific benefits for them.