Where to look for internships

To be in Year 10, you would be 15, correct?  Aside from your very young age, which is a huge obstacle, what kind of skills would a 15 year old have to offer an employer?

Although I am young, I have been in an international school for 10 years so I am extremely fluent in English and also, I have a lot of interest in Biology. The intern opportunity does not need to be medical related, I could help with translations between English and Korean. Also, I do not expect a salary, I can do it for free as a part-time job.

I am also fluent in Korean and can speak a bit of Spanish and Japanese.

It's very good that you're bilingual, but unless you have connections in a Korean company doing business in Hanoi, or any company that does a great deal of business with Korea, there's probably not a huge demand for Korean-English translator.

Also, your age is still a negative factor even though 15 is the minimum age for restrictive employment.  There are A LOT of restrictions in hiring a minor.  For instance, it's forbidden to hire a minor in any position that may expose him/her to chemicals, gas,, flame (lab burner and kitchen stove included), any equipment and machinery, any jobs that are detrimental to his/her health. 

Employer also must keep a detailed log on your working condition and must provide you with routine medical care at their cost to make sure your health is not jeopardized by the job.

Those are only two sentences out of a very long list of forbidden things indicated in the Labour Code 2012 regarding child labour.

I seriously doubt you would be able to find anyone willing to jump through legal hoops to give you a job (volunteer and internship included).