Ok , please forgive me on the lack of opensuse knowledge.
Before we get you running fully, the issue that you are having is that you have created a local grav installation under your home directory.
This makes grav have a bit of spat (not sure why).
We can get you up and running first then deal with how you actually are going to use grav & apache etc.
There are two options of installation.
One at the root of suselinux install or at a home level directory
They will require a few little pre-requisits and this is the method I used to get running (sorry if it look like, I am telling you to suck eggs)
php
I made sure that
php7-apc, php7-bz2, php7-curl, php7-exif, php7-fastcgi, php7-fpm, php7-gd, php7-gettext, php7-iconv, php7-json, php7-lzf, php7-mbstring, php7-openssl, php7-pear, php7-phar, php7-sockets, php7-tokenizer, php7-xmlreader, php7-xmlwrtier, php7-zip, php7-zlib
Now open an xterm up and use the su command to access as root.
su root
Enter root password <password>
The text will turn red to show root was succesfull (ie the password was right)
Next thing was to ensure composer was installed and upto date
composer self-update
then
composer -V
should report back v2.0.14
composer create-project getgrav/grav ./grav
this will install grav to a folder called grav in the home directory
we now want to change to that directory
cd grav
we are going install the admin gui package for easy of use, so type
bin/gpm install admin
Should prompt to install (Y)
after that is done, we are going to use grav testing server
php -S localhost:3456 system/router.php
Now the terminal window will be running a testing enviroment, leave this running.
If you stop it or close it down, it has been ran again as admin / root level user
so now open your browser window
enter
localhost:3456
you should be now presented with a working grav admin screen.
The issue that I found was that a php session handler that grav requires cant be run at a user level , it requires higher privildges hence why you need super user access.
If you get up and running and report back any issues, we can go from there to looking at how you want to run your enviroment (a lamp stack, apache etc) but to test you do not need it. Just that su php -S command.
Didnt have to alter any permission.
HTH and gets you on your way 