Are there any unhealthy situations in Mahabaratha?
As mentioned in Puranas (such as Matsya Purana, Kurma Purana, Vayu Purana..) and in Mahabharata, there were very less or no disease in Satya Yuga or Krita Yuga and in Treta Yuga.
Disease came to be known in Dvapara Yuga and it affected few people in Dvapara and it's widely found in Kali Yuga.
We can see few instances in Mahabharata where some one had disease. For example,
Vichitravirya died due to phthisis/tuberculosis/yakṣmā. ~Discussed in How did Vichitravirya die?
We also find few references of dropsy, leprosy and few other skin disease in Puranas.
So, there were few unhealthy situations in earlier Yugas and/or in Mahabharata.
Are there any slokas saying that their lifestyle is responsible for such diseaseless life?
Vayu Purana - Chapter 8 deals with this in detail. From abridged version of Vayu Purana,
In Satya Yuga, people lived on juice that came out of the bowels of the earth. This juice was so miraculous that old age and disease were unknown.