Hey guys!
I cannot find the option how to create a blog page and add the filter above the blog posts with a login as well as a search function. Anyone can help here? 
Wix Blog is a Wix app, you are best suited looking at Wix Support’s own Blog pages here.
https://support.wix.com/en/new-wix-blog/setting-up-the-new-wix-blog
Or contacting Wix Support here.
https://support.wix.com/en/article/contacting-wix-support
You can add the login bar as shown here.
https://support.wix.com/en/article/adding-a-login-bar-to-the-new-wix-blog
Or add recent or display posts as shown here.
https://support.wix.com/en/article/adding-a-recent-posts-element-to-the-new-wix-blog
https://support.wix.com/en/article/displaying-posts-on-multiple-site-pages-using-a-custom-feed-in-the-new-wix-blog
As for the search bar, then you will need to create this yourself and try to query the blog collection, making sure that you use the correct filter for whichever field you wish to filter through, providing that field can be filtered itself. Also, note that some of these fields can’t connect to data or be sorted too, so you might be able to use all the fields that you wanted too.
https://www.wix.com/corvid/reference/wix-data.WixDataQuery.html
https://support.wix.com/en/article/corvid-wix-blog-posts-collection-fields