As you are new to ML, I will try to explain in my simplest way.
1. I am unable to figure out how to make such conclusions with feature study in neural networks or other machine learning techniques.
Machine learning has many applications, what you are talking about here comes under the term Inference. It means to understand- how your output is affected as your input changes. I suggest you follow the book- An Introduction to Statistical Learning with Applications in R. On page 19 of this book, it is given-
We are often interested in understanding the way that Y is affected as X1,...,Xp change.
We instead want to understand the relationship between X and Y.
- Which predictors are associated with the response?
- What is the relationship between the response and each predictor?
- Can the relationship between Y and each predictor be adequately summarized using a linear equation, or is the relationship more complicated?
I have not posted the whole thing here, just some important points.
So here, instead of prediction, you just analyze your model. After analyzing you can make such conclusions.
2. Is there a way to quantify the likelihood in ANN similar to logistic regression wherein regression coefficients give the change in the log odds of the outcome for a one unit increase in the predictor variable?
As far as I understand, ANN has multiple layers. It is not like logistic regression which just defines one coefficient for each predictor. In ANN, the coefficients are defined for each layer separately, and in each layer, for each node.
Hope this helps.