As far as I know none of this is your fault so the landlady/lord will have to pay for all the repairs since he owns the property (it's in his best interest in the first place). Also, it shouldn't have an effect on your security deposit since again, it's not your fault. If you have a party and break all the furniture then you would lose your security deposit.
I came home Sunday evening after a weekend trip away to find that my andol and hot water is not working. I can turn on my water and it flows well when the faucet is on cold. If I turn the faucet on warm/hot it is at very low flow almost to a drip. Any ideas on what caused this? Frozen pipes? Bad boiler? Also any idea how to fix this would be great.
You're absolutely not liable for frozen pipes. This can be expensive and is completely upto the landlord. Have your Korean co-teacher speak to the landlord about it.