You didn't know that scammers, thieves, and malware exist? What world do you live in? Sounds like sig-ad nonsense to me.
No. Not fake electrum address. Fake software.
Thieves and scammers create fake software that looks like the real software. Then they try to trick people into downloading and running it.
This is ALWAYS true of ALL software that you download. Not just Electrum software. If you run software on your computer, you are giving that software access to the stuff that is on your computer. You always need to be careful.
It might.
VERY unlikely.
No. they don't.