No Bitcoins are lost, that's why it's called a "fork".
Think that it's just that the blockhain will follow a new route(using Classic mining instead of the actual one).
Misleading advice from a sig spammer, who'd have guessed?
will I then lose my Bitcoins from the Core version?
No. Coins mined before the fork can be spent on both chains (which, incidentally, allows double-spending, which is one of the main reasons why anyone who knows anything is totally opposed to hard forks except where absolutely necessary). Coins mined after the fork are only can only be spent on the chain on which they were mined.
Or will I rather be able to copy my wallet file from Core version to Classic and still use all my resources?
Yes.
Also, once the wallet file is replaced and my Bitcoins are compatibile with Classic version, are all funds from Core version gone/unusable?
As long as coins are not double-spent as explained above, you can spend coins from either wallet.
you forgot to add the point that based on pools adding new blocks, only one chain will survive based on which rules accept which blocks to make one chain the longest.
stop thinking that it will cause 2 forks that would continue forever.. consensus and rules orphan off blocks that dont fit the network
afterall if the network was to let "weird" blocks continue.. we would be having 2 new chains created each day
in short the network sorts itself out and we all follow the more popular chain (spoken in laymens terms)
in such events exchanges and other merchants wont accept transactions with zero-6confirms. but would wait maybe 10-20 confirms to cover the orphan risk that would increase.
if your transaction happens to be on the evential orphan blocks. then the result is as if the transaction never happened and the funds are still on your private key