What exactly is fork? Or Hard fork?
think of fork as a change.
https://en.wikipedia.org/wiki/Fork_(software_development)
bitcoin is a set of codes and rules known as consensus rules, usually in bitcoin when you change those rules we call it creating a fork. sometimes it is done to fix an issue (bitcoin's first hard fork years ago) sometimes it is done to add some features or "upgrade" like SegWit or previous fork for adding P2SH.
other times you can change these consensus rules to create something new. like changing block time and mining algorithm (litecoin), block size (bitcoin cash), mining algorithm (bitcoin gold) and lots of others. we call these altcoins.
sometimes these use bitcoin code only like litecoin and sometimes they also use the blockchain like the other two.
I heard that those who own bitcoins before 25th Oct will receive Bitcoin Gold. How does it actually work? Do I receive Bitcoin Gold automatically in my electrum wallet or do I need to do it manually?
they set a block height (491,407) and anyone who had any amount of bitcoin before that block will receive the equal amount of the new coin (BTG). it is because they will use the same "database" (blockchain) and the same keys.
so in your wallet as long as you have the private keys (which you do when you use electrum) you have the coins. you use the same key to spend them on the other chain.
And if I have 0.12 btc how much would I receive in bitcoin gold? And does the value of my btc change ?
you already have 0.12 bitcoin gold too.
bitcoin price may or may not change because of it!
