Where are coins stored when I'm not online and sent
The coins are "stored" in the blockchain.
Electrum holds the keys that can "unlock" your ability to spend bitcoin you have received.
Electrum (and every other wallet) DON'T store coins. They only store keys. That's a common misconception.
In order to "receive" coins, you need NOTHING at all. Just give someone an address.
You need Internet in order to:
1. Monitor your incoming transactions and perhaps get notifications about them.
2. Broadcast transactions a.k.a "send coins"
You don't need Internet to:
1. Receive coins
2. Sign transactions (assuming you will broadcast them later)
3. Create new wallets aka new pairs of keys
I hope I have answered your question. You don't need Internet to receive bitcoin. Coins are stored nowhere. That's not how it works. If someone wants to send you coins, they have to broadcast a transaction and let people (other nodes and miners) know that they have sent the coins. Once you open up electrum you need Internet to "see that you have received the coins".
This is amazing. But as far as I am trying to understand the balance is not updated unless and until it is connected to the internet right? Basically, if I am not looking at my wallet and only scanning my address over the blockchain then I can see the updated balance.
Which is a similar thing I am doing with Mycelium.
For example, the smartphone on which I have Mycelium installed is always turned off for safety reasons. I keep getting payment on that address, which is obviously getting synched in the background (without internet obviously).
Then this makes no difference to any wallets I believe.
I thought we already invented a technology that can work without the internet. I was shocked for a second after reading all the replies. It seems it's just usual thing, you synch up when you are online. Thats all.