Ok. I would suggest that your difficulty is due to the fact that your models (e.g., linear regression) is not well-suited to your data. You have already plotted data['TOTAL_CONV'] and it’s clear that it’s very (very very) skewed. So a model assuming normally distributed error is not going to go well and neither is a Student T (both are symmetric and thus won’t deal well with the skew).
I would probably step back and try to figure out exactly what you want out of your model. If you want to try an predict the continuous variation in your outcome variable, I’m not sure the data will be of much use to you (you don’t have enough variability ). If you instead could get by with predicting a dichotomous version of your outcome variable (e.g., data['TOTAL_CONV']>1), then you might be able make a bit more headway with the data you have. But it really depends on what you need.