1) The question is probably trivial, but what can be done after creating a full-fledged project? (version 1.4)
You can do whatever you want with it. Sell it, gift it, whatever. At the least on PC platforms, you should be fine with compatibility for quite a while, unlike the mobile platforms.
2) Are there any rules for publishing your projects, where can you go to get noticed, where can you publish, on what conditions? (I will have a project in 3d)
There aren't any rules as far as Yoyogames is concerned. You can publish however you want, your own site, Steam, Epic Games, whatever. The catch is you have to comply with the rules for wherever you sell. That is not anything to do with the Gamemaker software though and applies to games made in any software that want to sell on those platforms. As far as getting noticed, you will want to read up on things like marketing, social media, and the like. There are likely other posts here where such things have been discussed in the past but you will need to search for them.
3) What will determine the further fate of the project?
YOU determine the future fate of the project, at least as far as what you control. I'm not sure what you are getting at though. But yeah, Yoyogames doesn't own your project or anything like that.
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All that said, I've recommended to you in the past to upgrade to GMS2. I stand by that advice still. I'm not saying you need to convert your current project over(though it isn't a bad idea either since most things are compatible), but for the future I'd recommend it highly.