Yes, but I believe certain personal details have to match on both accounts, some of which are un-editable. Not for sure on specifics, hopefully someone else can comment.
I merged my F2P with my P2P some time ago, the F2P being under a completely made up name and email created specifically for the account, it took some time but it's possible.
And if you have the same name on both, should you contact a GM or can you do it manually in website?
The easiest way to go about it (in my experience) was actually to call Blizz and get somebody on the line to talk to, and explain your situation and what you're trying to do. The guy I had on the phone didn't understand why I wanted to merge a F2P account (going on about the restrictions, etc.) but I just told him I had obtained a mount that I wanted to my P2P account.
Was anyone successful with the same but fake name in the accounts? I dont have an ID with the names used .
See above.
1. Can I add the Battlechest to my account without accidentally upgrading the Starter Edition? If yes, how? I would rather quit than gearing up level 20 characters again.
2. If 1. is possible: is that meaning these two versions will be linked?
3. It isn't clear to me how could I log in with same email & password? How could I choose between these two versions when I want to play?
.
1) You'll have to make a separate P2P account, and then merge them AFAIK.
2) Assuming step one goes off without a hitch, yes.
3) When you go to log in, you'll have the option of choosing WOW1, WOW2, etc., the names of which correspond to the P2P or F2P account.
Here is an explanation of the steps I took to merge my accounts.
1) Called Blizzard, got through to WoW customer service and explained that I'd like to have the accounts merged.
2) You may have to explain your reasoning as the guy I was talking to didn't seem to understand what I was trying to accomplish.
3) Afterwards, you'll need to provide answers to questions about your P2P (main) account, such as the password and security question.
4) Finally, they'll need proof of identification, to make sure you're the same person that the account is under. For this step I emailed a scan of a piece of photo ID.
5) Voila, you've done it. You should receive an email or call back from the customer service guy to confirm that the accounts are merged.
Disclaimer: I'm not sure how the process would go if both accounts are under fake names. It would definitely take more time and hassle, of that I'm sure.