First of all, it will be good to read about how TrustedCoin charges 2fa fee if enabled on electrum wallet, to know if to use it or not. If you think the 2fa fee is high, it will be good to create a standard wallet, you can also use segwit which will charge you lesser fee during transaction.
https://api.trustedcoin.com/#/electrum-helpBasically, if i understand things correctly, only one for bitcoins, the BTC. But I dont see the "BTC(SegWit)" there. However, when i go to the Deposit - Crypto page in binance, there is one extra Transfer Network there. SegWit! Binance has 2 BTC Networks to choose from when you want to deposit, but only one when you want to withdraw. And that one is the expensive one! I dont understand it...
Binance support segwit for deposit, I do not know if the withdrawal will be segwit or not, but it does not matter as the fee is static at 0.0005BTC which is already too high for even legacy address transaction to be confirmed in the next block, you can deposit from segwit to legacy or legacy to segwit or to any bitcoin address, so far it is bitcoin address, the transaction will be successful. So, just use the withdraw to send to the segwit address, it will be successful.
If i choose the "BTC" transfer network to withdraw my bitcoins and deposit them into electrum and pay the heavy fee price of 0.0005 BTC / 20 dollars, is my Electrum's address safe to use even if it starts with bc1 or im going to lose my money? Does the network have to be "BTC (segwit)" ?
Your bitcoin is safe. Make sure you use BTC, (do not use BEP2 (BNB), BEP20 (BSC), ERC20 (ETH))
Lastly, why is the fee so expensive? 20$ seems a quit a lot. Am i doing something wrong...? Is there another way to minimize the fees? Should i create another wallet?
Exchanges do charge high fee, some even charge higher than Binance. You are not doing anything wrong. There is no way to minimize the fee. You do not have to create another wallet unless you do not like 2fa because of the extra fee charge, and in that case, opening normal segwit wallet on electrum will be good, but that does not change the fact that Binance will charge you 0.0005BTC as electrum is not responsible for that but Binance.