Why don't you download all the engines that might match your criterias (hint: you most probably can count the ones in financial reach on one hand, Unity is a t the forefront for sheer size of community (as Unreal doesn't seem to support HTML5 yet), and test them all out?
With the amount of information you are giving (or lack thereof), its gonna be hard for anyone around here to give you a recommendation tailored to your project, and really, depending on your project and what you REALLY need (As opposed to what you now think you need), a lot or no game engine could fit.
1) have a look at the engine DB on devmaster.net... maybe you see another engine you haven't heard about before on there.
2) Maybe explain in detail why Unity is not a good fit for your project... if you are REALLY serious about targeting all the devices, you WILL kill yourself with coding in support for that if you do not start from a good baseline. Unity is most probably as good as it gets when it comes to targetting different devices.
3) Networking: there are many options, if you go with Unity, have a look at the asset store. Some of the frameworks can even be downloaded for free (but then will of course force you to go through their servers / cloud service)
Be aware that AFAIK, there is no one-size-fits-all solution for networking yet. Even with a framework, you get basically a glorified chat server and some low level plumbing layers that give you high-performant building blocks to build your own server and networking layer with. This is a highly technical programming project though, that will need an expierienced programmer though!
If you are really serious about this project and that you need a multiplayer, make sure you plan in enough time for it, and attack it with the right expectations: You will have to get your hands dirty here.
And yeah, I'm asking for a lot and I'm not even sure if it's needed.
I'm new to publishing game and making games for the public I only made some games in unity etc for myself but now I want to to a step forward by making a big game.
I don't even mind if it's never gonna be released or something I just wanna learn from it and have made something awesome and big instead of only small trial games and projects.
If you're really serious about making money you're probably going to want to focus on mobile, it has the least entry requirements by far. Even a game like goat simulator that sold well on desktop by virtue of basically being a fluke, still took a team of more than one person(as far as I know.)
Most developers completely lack the ability to polish a game, that tends to stand out a lot more to employers and such than a bunch of tech demos because it shows you have a knack for detail, stuff that makes them more money.
Any evidence that supports your notion "concentrate on mobile to make money"? AFAIK, mobile space has become a highly competetitive one where even AAA games cannot ask for more than maybe 5-10$, while the amount of low level crap games flooding the app stores that are free is staggering.
If you ask me, PC has the lowest entry requirments. But I also have no evidence to show, just personal opinion. You can get lucky on mobile of course, like flappy bird. But we are talking about one game out of a billion released. Goat simulator took more than one person to build, sold as much, while being a one out of a million lucky hit maybe.... yeah, your chances are not much better, but really, game dev IS a highly competitive field, so don't expect too much either way
mobile app stores are flooded to the brim with games, and income per sale is much lower. On the PC side you have to find your niche, use the Indie / Boutique game craze going on at the moment, and find the right outlet (Steam, if you can make it).... still, you could ask 5-10$ for a game that you might not get 1$ for on mobile, and still some people would pay it, if the game is good enough.
All personal opinion, of course.
100% agreed on the second part though. A finished and polished product shows dedication, expierience and a 'get-it-done' work ethic that a lot of people nowadays lack.
I know how much work it is to make a game but I also know how difficult it can be to think of unique gameplay nowadays.
During my study I learned basically never to share your ideas in public, as ideas can't be copyrighted and products can.
If I put up the entire game design/concept I'm sure nobody will make it like that but I just don't wanna risk it as I have spend quite a while coming to this final idea.
But as I said for any specific questions towards the game I don't mind sharing I'm just not gonna put up the entire concept.
Secondly I don't have to earn any money from it at all.
The only thing I mentioned was a kickstarter for Unity pro and other licenses.
My main goal for this game is to learn how it works to make a big game from start to end by publishing it.
And of course I love making games as it's my job and passion.
See it like that:
Most people capable of snatching your idea, turn it into a working game AND good enough to finish it, most probably are busy with their own ideas at the moment.
Sad story is, no matter how good you think your idea is: without the execution its worthless. Nobody will pay you a penny for it, and most people will think its crap. Because they might not understand the same thing you do from your written notes. Its ONLY the execution, how you turn this ideas into a working game, that counts.
If you learned not to share your ideas then you learned something wrong. Keeping ideas close to your chest until they have evolved into something good is a brilliant idea. Keeping them from the potential client until have something to show that gives a good first impression is wise. Not sharing it with people you are asking for help is not so a good idea.
Always share as much as you need to, of course. No need to go into detail about your exact implementation if you are just looking for general guidance on your story idea, or a single gameplay system. But really, sharing ideas can be a wonderful thing. The game dev community wouldnt be were it is today without people that, at a convinient time, shared ideas they kept close to their chest with others. Without all the blog posts where an expierienced dev shared how he implemented feature X in game Y or pot-mortems showing how they did game Z, becoming a game dev would be much more expensive and harder for people.
And all the sharers get free exposure and advertisment for their upcoming or existing games in return, AND they might be using things other devs shared the same way.
Anyway, TL; DR;
It is your choice how much of your ideas you share. Chances are very good nobody here will steal it, as turning an idea into reality is the hard part, not coming up with the idea. Chances are everyone is busy with their own ideas, or you idea is just not good enough to be stolen.
Just because you release some information about part of your idea, high level concepts and so on, does not mean you have to put your GDD on this forum. Nobody is aking for that to give you general guidance.