When you say high risk to get the usb-stick infected, do you mean like 0,1% or 10%-90% ?
I didn't mean to make it sound like it's likely to get it infected, but I generally avoid moving crypto-related stuff through removable storage devices such as USBs and MicroSD cards. At one point, it's possible that you may not wipe the USB correctly and plug it into an infected PC while still containing your .dat file.
Its a new formated usb-stick btw.
I don't see it as a problem
now, but for the longer-term. Once you get used to the convenience of moving files through USB from one device to another, you get to prefer doing that rather than safer methods.
Yes, we have been writing both the wallet-address and the private key down on a piece of paper.
That's great. The private key is enough for your backup, but it's certainly not bad to also have the wallet address written next to it.
If we would use the option "Import the private key straight from the initial Electrum setup", is that the same thing as if we would import the dat-file in another bitcoin core, or just adding the address and privatekey inside that program?
By using that option, you'd only import the private key inside your wallet. As in, you'd only have an Electrum wallet with a single address in it that you can use.
Its the same wallet just that we can open it from another app?
No, importing the ".dat" file and importing the privkey are two different things. AFAIK, the privkey is
part of the ".dat" file. It's the access to a
single Bitcoin address that you've exported from your old Bitcoin Core wallet.
By the way, are you sure you only have a
single address that you've used on your old Bitcoin Core wallet? You can generate multiple receiving addresses, so make sure you backed up the good one(s).
Enter a list of Bitcoin addresses (this will create a watching-only wallet), or a list of private keys.
Here we are writing the wallet-address, right? Like:
p2pkh:WALLET_ADDRESS
No. If you enter just the
address, you will create a watch-only wallet. You can watch
anyone's wallet - even mine. If you insert my Bitcoin address in there, you could see my txs, my balance etc. but you do not have access to spend from my address. It's like I'd show you a number of physical banknotes. You can see them, you can count them, but you can't use them because they're mine.
In there you only have to insert the
private key. As I said above, the privkey is enough to recover your funds.
When do you add the privatekey? And will this be stored on the new computer anywhere? This option is like import the same wallet inside a new app? Nothing new is happening? This will also continue the sync?
Assuming it's a new PC, the sync will not "continue" from the point your old PC's Bitcoin Core has reached. It would just start from zero instead. But as I mentioned, when you use Electrum, unless you're running a full node (downloading and syncing the entire blockchain, like you had to do with Bitcoin Core), the sync will only take a few seconds. It's running in light mode by default, which means you don't need a lot of storage and time to sync it.
But in all honesty, considering that you are quite new to this stuff, I would rather recommend either
sweeping all the private key(s) or fully syncing the Bitcoin Core wallet as @HCP suggested above and having your entire balance be up-to-date before actually moving funds out. You may have other receiving addresses you've used before and still have balance in them. May take more time, but better be safe than sorry.