I want to create a webserver local-network accessible but without router. The idea is to connect a device (phone, PC) to the Raspberry over WiFi, and see the webpage on the Apache Server.
Is it possible?
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Yes there should not be a problem having the Pi run apache and be the access point as the Pi will act as a device on its own access point allowing the apache server to seem as if it is running though a router.
Complicated multipart question. So let's break it down.
First, of course you can run a web server on your Rpi. Whatever else it is doing with its networking doesn't affect that part.
Then, you talk about adding a generic device. Your examples of a PC and a phone are dramatically different.
There are other posts on this web site that talk about making a Rpi media server. I strongly suggest you do more research before posting a question like this. Spend some time in the archives and you will likely find your answer.