I'm now 18 and I'm wondering if I still get the penalty for overstaying in the U.S for over 180 days even if I was a minor.
The accumulation of unlawful presence for determining statutory inadmissibility does not include periods of overstay when one is a minor. See 8 USC 1182(a)(9)(B)(III)(I):
No period of time in which an alien is under 18 years of age shall be taken into account in determining the period of unlawful presence in the United States under clause (i).
If not am I eligible to apply for an ESTA?
You are eligible to apply.
or is there a chance I get declined because I overstayed?
There is that chance.
If I do somehow get an ESTA is there a high chance I get deported when I go through immigration?
No. If you get an ESTA after answering all the questions truthfully, you can use it, and you're unlikely to be refused entry for this reason. If the ESTA is refused, you can apply for a visa (provided the consulate is accepting such applications), which will probably not be refused simply because of the overstay. You should, however, be prepared to show that you did not overstay voluntarily, because you were a child, and that you have a solid reason for going back to Korea. If you don't have a clear reason to return, your visa application is more likely to be refused.