1) I'm wondering if I can confirm the transaction myself, by doing the ~1 hour of compute on my computer ?
Bitcoin transactions are confirmed when miners include them in a block. There is no way to confirm a single transaction short of mining yourself, which is virtually impossible with a personal computer.
Divide your transaction's fee in satoshis by its size in bytes, then compare it with the
recommended fee rate to get an idea of when you can expect a confirmation.
2) is there a way to avoid to lose fee when we transfer money between 2 wallets that we own.
Bitcoin doesn't distinguish between transfers to another wallet you own and transfers to other addresses, so the fee cannot be avoided. However, you could import the private key of the first wallet into the second, which doesn't really transfer the funds but gives both wallets access to them.
