You're asking quite a few questions at once and they're pretty open-ended, so it's hard to properly answer them all, as I see it, but I'll do my best
Regarding the "Which is the correct manual" one.
I'd suggest to always start with the official documentation available in Help Center https://www.ptc.com/en/support/help
Here are the links for installing ThingWorx Foundation and Experience Service
https://support.ptc.com/help/thingworx/platform/r9/en/index.html#page/ThingWorx/Help/Installation/Installation/installation.html#
https://support.ptc.com/help/vuforia/es_install/en/#page/ES_Install_Help_Center%2FThingServerInstall_Installation.html%23
https://www.ptc.com/en/support/refdoc/Vuforia_Experience_Service/latest/ESInstallDeploy
Regarding "Why there is no installer for thingworx?"...
There is one, and it has been available for quite a long time, at least starting with 8.5, if I remember correctly.
https://support.ptc.com/help/thingworx/platform/r9/en/index.html#page/ThingWorx/Help/Installation/ThingWorxInstallers.html#
You still can opt in for doing things manually, the old school way
Regarding "Where i get thingworx url?"...
The answer will be pretty obvious after one has completed the installation.
Normally / by default it's something like http(s)://<hostname>/Thingworx
The last one, "How do i check if Thingworx is working?", is pretty open-ended and the topic itself is rather complex - there are different approaches to health checking / monitoring software in general and ThingWorx in particular.
In the simplest case, one just opens http(s)://<thingworx-host>/Thingworx url and sees if Composer UI opens.
Or you can check particular API endpoints, like http://<vuforia>:2019/ExperienceService/ping for Experience Service
I'd recommend reading this TS artice https://www.ptc.com/en/support/article/cs347564
