can we trust feature importance of a poor model Usually when training ensemble learning algorithms or a regression model we calculate feature importance and make conclusion that feature with highest feature importance has largest affect on y-variable.
No doubt when model itself if reliable(High MSE or accuracy) however what if model is not performing well? Can we still trust feature importance?

The key consideration is that feature importance is always an importance for the particular model and the particular dataset. There is no such a thing as global importance. If you use different feature selection algorithms, you can expect that they would pick different features, hence consider different features to be important.
So if you have a poorly performing model, than feature importance tells you that the feature is important for the model when it makes its (poor) predictions. It doesn't mean that there is no other, better performing model, that possibly assigns less or more importance to the feature.
