How to normalize a table with common and non-common fields

What you are proposing is a good solution for your requirement of M:N products to categories and hierarchical categories.

To avoid exposing yourself to numerous updates: You need to do two things to ensure that you don't have a lot of updates in your intersection table.

First, you need to be sure that your categories have a stable, persistent primary key.

Second, you need to link food items to leaf categories. Don't join Cherry to Red, Healthy, Fruit and Food - just join it to Red and Healthy. Your nested sets take care of all of the secondary (and higher level) associations.

I think the benefit of having a common table for blog, video, gallery, comment is that you will have unique id for each one of these, but that is really not needed.

And It seems that all these share some common attributes, so we need to have common table to save those, but from application point of view they will be different and needs to be save in different table.

Saving all of them in common table will be problem in maintainance, and also while fetching those entry to show in UI, So it would be better to have different table for all these four.

Then there comes thing is how to store comments, Well comments can be on video or blog or gallery, and with time it can be very large in numbers so you can choose one comment table for each category.