I kept my Bitcoins on both Blockchain and in Kraken at the time of forks.
If they didn't give them to you yet, you can forget about all Forks for coins held at an exchange.
Forks at your own Blockchain wallet can be recovered.
Is the private key the same as seed?
Not really: a private key gives access to 1 address, the seed gives access to all private keys for all your addresses.
I have looked online at ways to get private keys from a Blockchain wallet, but they all mention the 12-word seed when you specially ask for "private key".
Depending on the wallet you're going to use, you may use the 12 word seed or individual private keys. Be careful though, compromised Fork wallets have been stealing funds, so I prefer not to trust online Fork wallets with either seed or private keys.
Or is private key here the 64-random code?
I don't now which code this is.
Also, what if the coins were on an exchange? How do you "export the private keys" exactly?
You can't. "Not your keys, not your coins". The exchange may or may not have claimed all valuable Forks for themselves, and some of them gave some Forks to their users.
Is there a step-by-step guide anywhere, because sometimes phrases are used that are not clear (like "export").
When I downloaded Electrum, I only found out later that you need to check the Encrypton Keys using GPA. But this was not known at the time. So is there a foolproof guide which really covers everything, so you are not told later "oh, you should not have done that" when you had no way of knowing at the time?
There are many guides, but I wouldn't call any of htem completely foolproof. I offer
a service for it though