inconsistent URLs

[M-4]

I'm starting the use prestashop and the urls are very inconstistent (which is very annoying and not how it's supposed to work - state mgmt is very very odd):

I have a test shop with 2 products and a few categories. I know that there's a certain url that shows some photos:

1. I go the the root url of my shop -> the search menu is not shown properly.

2. I add to the url `/3-photo` -> I get the (faceted) search menu

3. I go to the root url -> I get the (faceted) search menu

I expect 1 and 3 to show exactly the same thing, since both are the same url (which is what a url usually is about: a resource). This is not the case. See screencast...

I'm not sure how to proceed, since I'm having quite some problems with making PrestaShop work properly - I've been reinstalling about a dozen times by now. I follow tutorials etc, but it always fails somehow. Is it just me, or are there really quite some issues?

Edited August 5, 2019 by M-4
another example (from an ok home to wrong just by browsing the faceted search) (see edit history)