C++ is the best option to programm such a game wich could get a bigger project, am I right?
Nope. It might be the best option, but that really depends on what languages you already know, what you mean by 'best', and how you measure 'big'. It's certainly the most widely used option (in large studios), but Eve Online was mostly coded in Python. Runescape is Java. Minecraft is also Java.
DirectX or OpenGL? Which is easier to use and which is faster for 3D graphics and landscapes?
DirectX might be easier to use, but they are about equal in speed, and DirectX only officially works on Windows.
Are there any engines that are made for creating games? Also under free Licenses like GNU?
GNU is an organization, not a license. GNU, the organization, has two major licenses: LGPL and GPL. Without getting into the technical details, GPL will make it a bit harder to profit on your game in the classical "I give you game, you give me money" sense.
So, assuming you mean LGPL, yes there are C++ LGPL (or better) engines available.
Torque 3D was really recently released under the MIT license. MIT/zlib/PNG licenses are about as free as you can get.
Crystal Space would probably be a good option, and though I can't find any licensing information, I think it's LGPL.
Are there any tutorials for building Login and/or World TCP/UDP Servers in C++ for an unlimited amount of players?
Do you already know how to program in C++? If not, you are getting way in advance of yourself.
Unlimited is also a very large number - it's higher than I can count, anyway. Most tutorials only teach the basics of how to do small servers (<100 users), and people use the knowledge gained through working on increasingly larger projects to build MMOs.
Is Microsoft Visual Studio Professional 2010 the right choice to programm such a game?
You don't need the professional version - the express version is perfectly fine for commercial projects, and isn't limited in the restraining ways most software 'express' versions usually are.
Are there any tutorials for structuring and organizing games?
Not too many, unfortunately. That is one of the things you learn through experience through the half-dozen full games you create before you create a MMORPG. MMORPGs are very very very difficult projects.
And I apologize in advance for my bad english.
Your written english is very good - almost perfect, so no worries.