Posting automatic updates to a Facebook page as a non-user page

I posted a question yesterday about posting comments created on Facebook using Java , but from the answer I figured out the question I need to ask. I want to achieve the following:

I have a Facebook page presenting a product. I can't figure out what it is, but I can imagine a scenario that relates to my problem. Let's say the product was a restaurant and I have a web page. So I want to link my Facebook page (for this restaurant) and the webpage that I have packaged. On my webpage, I have the following functions. Every week one of my services selects 5 menus and makes them advertisements and displays them on the home page. Now I want these 5 menus to be published on the Facebook page that I created for the restaurant automatically. It is clear that no one will manage this publication, it will be done using the web application. Because it's automated, I don't want to prompt anyone to log in to Facebook every time it does.

First of all, can this be achieved? or there are some restrictions from facebook that forbid this action.

If so, can someone point me to a Java example where this is done.

So far I've created a Facebook app, so it has a page for it. But when I did the actions I pointed out in posting the comments created with the app on the Facebook page using Java , the message was not displayed. I was able to post a message from my app to my profile saying the post was done through my app, but that's not what I'm looking for.

If all of this can be achieved, could it be done with RestFb as an API?