This is the fee I paid for the transaction. 0.0007164 BTC ( 31.4 sat/byte ) [...] When I change the value, Electrum gives me a new one, like 41.1 sat/byte.
That's very little if you take into account the current state of the mempool. Take a look at the third graph on
this website. A 80 sat/byte fee should get your transaction confirmed in about 5 blocks while 100 sat/byte in only about two.
When I change the value, Electrum gives me a new one, like 41.1 sat/byte. I just confirm but nothing happens. Do I need to change the option to Mempool, Estimated Time (which is set as default) or Static?
These are the fee estimation methods which become irrelevant if you specify the fee manually. I am using Electrum with my hardware wallet, so it might be a bit different for you, but after I confirm a new fee, a new window shows up where I need to press "Sign" and "Broadcast" in order to replace the transaction.