My question is exactly about the network fees. Is this the right method to do it, the one I mentioned above? I have seen that you can "sweep" the chips into Electrom - are there any fees for that? Thanks!
You can use this site to determine the current transaction fees of the Bitcoin network,
https://mempool.emzy.de/ and use this
Bitcoin Fee Estimator / Calculator for you to identify which fee has a faster transaction speed according to what you want, the higher fees the fastest transaction will make.
Probably you mean Electrum wallet and make sure you're on the official website,
https://electrum.org/#download, and verify this as the instruction on the site. Yes, all wallet that supports SegWit address will modify the fees and reduce it to the cheaper one and it varies to the transaction speed.