OS X Base System only disk available
I found an old thread but it did not solve the problem, after the internet recovery it says recovery cannot be found.
It appears your second picture is showing an internal Hitachi hard drive. Not sure what you are trying to do here since you have provide no details. Maybe if we knew exactly what you were trying to do we could provide other suggestions. FYI, it makes a difference whether you are trying to reinstall macOS over top of itself (helps to know the version of macOS currently installed) or a clean install.
The first picture you posted regarding "The recovery server could not be contacted" seems to be a common problem recently. Seems Apple is having problems with their older online macOS installers. I'm not aware of any way around that error at this time.
Do you have access to another Mac from about Late-2009 to 2018 that you can use to create a bootable macOS 10.13 USB installer using the instructions in this Apple article (it would bypass the server error):
Create a bootable installer for macOS - Apple Support
If we knew the exact model of this Mac, there may be other models which could be used to create a bootable macOS USB installer for a different version of macOS. You can get the exact model by entering the system serial number here:
Check Your Service and Support Coverage - Apple Support