Service Battery issue My battery is in 'service-required' state since couple years back. I am in South Korea and the first apple branch will open in Seoul in March this year. I wonder if this is part of the reason why it takes so long to retrieve the needed components as they say. 

It was to take about 10 working days here to fix it, at the cost of apx. 200 USD. More because of the time, as I'm heavily dependent on the computer I understand so little, I decided to stick with it. It turns out I have another friend in the same situation in this country. 

It's uncomfortable that the laptop has to be connected to the cord at all times, but without it I have troubles to deal with anyway. I found out about the kits provided by iFixit, but they don't ship overseas. Plus, lithium-ion batteries have special rules at the customs of the airport; not a daily convenience stuff to ask for friends to smuggle in when they visit for holidays. 

So I have been wondering for quite long, if you take it to an apple branch in America or other countries with good industrial network, how long does it cost to fix this state?

I currently use Macbook Pro of 2012. (OS: High Sierra 10.13.2)
Wait depends on two factors: a) whether the Apple store or the service provider has the battery in stock; wait for delivery from Apple is probably a day or two; and b) the existence (or not) of sufficient techs at the store or shop to do the work that customers have ordered. If work is backed up, it'll take longer.

A battery change should take .5 - 1 hr, and if the customer is lucky (i.e., battery in stock and a tech available), might be able to be accomplished while the customer waits.