Opinion only follows: adjust to taste.
Webcontrol is a web server system. It can run on anything, but it makes a lot of sense to run in on a dedicated computer. Many people use a Pi for this. I do also.
Internet access is not required at all for webcontrol to run. If you want to update webcontrol it is useful. This update can be done using other methods though.
Since it is a web server, it has to “listen” to some IP address(es). It will, by default listen to every address on the dedicated computer. Certainly it will listen to 127.0.0.1, and if you have other networks defined, it will listen to them, as well. 127.0.0.1 is only available from other tasks running on the Pi, though. I recommend that you set up a 192.16.xxx.xxx network on the dedicated computer solely for the use of webcontrol. And that this network not be the one that you use for wifi.
There are two reasons for this. First, security. webcontrol does no authentication. Anyone who can reach port 50000 of the computer on which webcontrol is running can do things to your maslow. I have seen far too many people accidentally enable remote access into their internal devices to be comfortable recommending that people use webcontrol on their primary wifi. If you do use your primary wifi, at least be sure that you block TCP port 50000 incoming on your edge device. Second, reliability. I prefer a wired connection. Wire will obviously not work for people who want to use a phone or an iPad as a controller. With a reasonably recent laptop, you won’t even need a switch, you will be able to directly cable to the Pi and the laptop and Pi will automatically adjust.
Finally, as to using the PI as both a browser and web server, it is possible, but I would not recommend it. Web browsers are fairly heavy beasts, eating up a lot of memory and CPU cycles. Moreover, webconotrol uses websockets to push data back into the controller. This constant updating adds stress to both the server and the controller.
Even though the Pi is, by historical standards, a capable machine; it is not the environment for which current web browsers are optimized. For the controller, find a used laptop, or a low-end chromebook. I use a pinebook pro. It won’t cost you much more than a monitor, a keyboard, and a mouse, especially since the Pi only supports HDMI which means you probably can’t use an old used monitor.
Final note: if you do use the Pi as both server and controller, it is probably best to simply forget about the iPad. While it might be useful for the z-axis, it comes at the expense of the server needing more memory and more cycles to build the extra session and to keep both sessions updated. Choose one or the other.