Thank you very much for your questions, Levi. I apologize for the considerable delay in approving your post due to technical difficulties.
1) We accept candidates from any nation that is normally allowed to enter Japan on the short-term visa waiver program or with an applicable visa, including the Philippines. Unfortunately, due to COVID-19, the Japanese government has temporarily suspended all visa application processing, and accordingly, we are currently not moving forward with overseas candidates. However, we intend to resume our matching process for overseas candidates the moment new entries are once again allowed into the country.
2) Under normal circumstances, those who are offered an internship will be provided with monetary support for basic airfare, housing, transportation fees, etc. Details vary between each position and are provided with an offer.
3) Under normal circumstances, the internship period of an internship-to-hire program would usually take place under a short-term visa waiver or another short-term visa type. Full work visa sponsorship is included with a subsequent full-time job offer, and generally falls under the wide "Engineering / Specialist in Humanities / International Services" category, unless another category (such as "Instructor") is applicable. Visas are handled on a case-by-case basis, however, so we consult with candidates individually to determine the best arrangement for them when the time comes.
4) The hiring company for the position you are offered would be considered your visa sponsor.
5) The application for a Certificate of Eligibility is typically handled by the hiring company/our office and is then sent to the candidate for their final visa application to their respective Japanese consulate/embassy. We also provide support with arranging all the necessary paperwork for a visa application when the time comes.
6) If it is not required for you to return home to accept your degree, you would not need to leave Japan for that particular reason. We would consult with you to find the best arrangement for you based on your situation, current immigration policy, etc., but if you were offered a full-time position post-internship, it may be possible to remain in Japan and continue working with a company until graduation.
I hope this fully answers your questions! Please let me know if there is anything else I can clarify.