B.t.w. I have contacted Binance - where my stolen BTC ended up on one of their addresses - and after proving (with screenshots, videos from wallet opening and wallet/TX history) that I am the owner of the address from which the BTC got stolen, they offered to refund me - but only if I open a Binance account (they will send it to my Binance address)! They said the owner of this Binance BTC address (obviously their customer=the hacker!) agreed to send it back!!! WTF

Has anyone had this experience?
This doesn't sound like a reputable Customer service, are you certain that you're talking to Binance?
If you can confirm it, then that's one good news already but it's certain that they'll ask for KYC data before returning the funds to you.
Has anyone had this experience? The don't want to give me his identity nor the type of attack how the BTCs got removed! This looks very dodgy and supports my theory of a malicious server attack / vulnerability in Electrum which they maybe want to hide...
Normally, they wont provide you anything about the hacker without the police/authorities' intervention.
For the attack vector, it's impossible for them to know which Electrum/PC vulnerability the hacker utilized to steal your bitcoins.
They aren't the developers of Electrum and auditing the code for unnoticed bugs is hard even for its developer.
Here's the list of vulnerabilities, click each for the affected versions:
github.com/spesmilo/electrum/security(
of course, unnoticed/unreported bugs aren't included)