Hey there Seodoa,
First I’m not a lawyer, in the US, nor any other country, hence this is just “layman’s” knowledge
Q1. Logo creation can be done very simply at many sites on the internet. What are the implications? Well if you wish to have the logo Trademarked, or as a ServiceMark, you would need to look into that as well.
Q2. As Epic Games has already copyrighted their Engine, you would not be allowed to copyright the engine, or any thing else that Epic provides (static meshes, art, etc), you will also be restricted by Epic Games, pursuant to the EULA, and any other documents that Epic Games may have as a condition of using the UE4 engine.
Q3. Copyright via the Berne Convention, occurs in two forms. Unpublished work, and Published work. The “Published Works” at least in the US have a much higher standing in Court. Especially if they are also backed up with an actual Copyright filing, etc.
Unpublished Works: Those works essentially where let’s say you have some source code for a program, and have put in some kind of Copyright statement. This is technically automatically copyrighted, via the Berne Convention again. Yet, in the US court’s, a judge is going, to not look on it, as being all that credible. You would still be better off, mailing a flash drive of the source, to yourself, via certified mail, and never opening the package at least. Unpublished can also mean you have never in any fashion sold the product your building.
Published Works: Those works that are available to the public for purchase, with the copyright statement prominently displayed, and all the rules about that as well. As well as an actual copyright filed, etc. This form of copyright protection is far stronger in the US.
As to a European Country, well that’s going to be two fold, in that is the European Country a member of the EU? This may or may not abrogate the laws of the Country even if it is a member of the EU, or one may have a higher standing in the Countries court system, if the Country’s laws are also followed as well as that of the EU.
You really need to talk to a lawyer in your country, concerning the rest of the questions.
Anyway, hope this helps,