I'm a Filipino mom and my partner is a Japanese, married kami in Japan, not yet in Philippines.
1st question: if we get divorce, is there something I or we need to do with my civil status in Philippines?
You need to submit a copy of your marriage certificate to Japan Embassy in the Philippines and NSO for your records in Philippines if you wish to secure your legality of marriage.
2nd Q.: what could be our benefits if we get marry also here in Philippines? Especially on his part.
You cannot remarry him in the Philippines again all you have to do is submit authenticated copies of what I already mentioned above.
3rd. We have a baby, if we get divorce, what shall I do to secure our financial needs or to make sure thAt he will still continue to support us? He is staying in Japan , and me and my baby stay here in the Philippines.
Again, if those documents are submitted to mentioned above, it will secure you and your baby in the future if you get divorce.