Advance Methods of Understanding Significance of Customer Behaviors
Welcome to DS stack exchange! Some of your questions/statements are not too clear, I'll try to answer to the best of my abilities but try to ask more precise questions in the future to get better answers (and avoid being down-voted).

To your points 1. and 2.: I would say it's highly unlikely that you'd be able to attribute a small fluctuation like 8% to just moving a button, moreover on such a short time span. And the question you should ask yourself is: "Is this the only thing that you've changed?". The fluctuation in point 2. could easily be attributed to effects like it being the weekend. Two things you'll want to look at to get you started are A/B testing and ARMA models.

Use A/B testing to show some of your customers e.g. a button on a new position or a new background color. Now check how likely they are to return vs. the batch of customers who saw the old design. If the new one is significantly better, then you can be confident that you should roll out the new design.

Set up an ARMA model to predict daily aggregate traffic. I'd advice against smoothing of any kind, it would likely be a bad idea. You first need to set a baseline which you do by comparing e.g. a month's worth of predictions with the actual counts. From this you can estimate the probability distribution of the errors you'd expect from your model. Now when you roll out new features/contents, you can see if the predicted traffic (which is based on data for the old website) is significantly lower that the actual traffic. If so, your new feature/content is a success.

Hope this helps!