Now i created a wallet on electrum.
Is this desktop wallet (electrum) has lower transaction fees when transferring to binance? And is this trustworthy?
BitMaxz has given answers to what you have asked. In addition to what BitMaxz has commented, know that Binance is an exchange and a custodial type that gives no keys which makes your coins on Binance not to be yours on the blockchain which makes you not to have complet control. The custodial exchange has the complete control which can be used to overide yours. Also know that custododial exchanges are hackers site if attraction, this makes your coins or your kyc that you are providing them not to be safe.
Electrum is a noncustododial wallet, it only required the fee that are paid to miners to make the transaction to be included in a block for confirmation. So you do not have to bother about the fee. As BitMaxz commented, you can even customize the fee on Electrum while making transaction, but in this regard, you will like to check this mempool observer to know the fee rate needed to make your transaction to be included in a block as fast as possible.
https://mempool.spacehttps://jochen-hoenicke.de/queue/#BTC,24h,weight