How to Add Search and Category Navigation for Blog
Go to "Sites" > "Blogs"
Once you go to Blogs from the list, click on the name of blog and in the list view of blog there is option to "Edit the Site".
After going to specific blog site editor, there will be option of in Elements of Category Navigation.
Drag and drop the Category Navigation element.
While editing, it allows user to add more category in navigation. For Example, click on the "Category 1" to edit the Category name and link to the category associated with the blog post. Please do the similar to other category options too.
For Adding the Blog Search, there is option to enable or disable.