So my friend sends .00685244 BTC, which was $77.
When i see it receiving into my Electrum, it is already down to .00570095 BTC, which is $64.
This is Coinbase's fee paid to the miners. Coinbase will always send transactions with the bigger fee required to get a confirmation in the next block, and which most of the time is exaggerated.
After checking your TX ID and the address linked to it, I see that the fee charged was probably 0.00115149 BTC or $13.59 as of now (511.773 sat/B). Next time tell your friend to transfer his Coinbase funds to GDAX (or just buy directly from there) and withdrawal. If you use GDAX, there is no fees to buy Bitcoin (so no $3 fee) and the miner fees are paid by them. You would have saved an extra $16 ($3 + $13).
Just search "save fees with GDAX" on Youtube.
Then, i send it from Electrum to my personal account.
After THAT fee, In the end, i get .00497707.
Again, miner fees. Electrum will suggest you a fee, but you can actually lower that value to one you are comfortable to pay.
So from transferring the coin from Coinbase to Electrum, and then Electrum to my personal account, i lost over 33% of my coin?
Sadly yes. Next time do what I said above and you will save a lot of money in fees. Also, I don't see why you did Coinbase -> Electrum -> Personal account instead of Coinbase (or GDAX to save even more fees) -> Personal. If you did the second option from Coinbase, you would have paid only 1 fee. If you did from GDAX, no fees at all. You would have received the whole $80.