What did Deepbit to make their inputs special on transactions? It seems Deepbit uses a strange format for it’s transactions on the addresses it owned. For example, in this transaction all inputs but 3 comes from Deepbit. Even Bitcoin core can’t decode addresses or scripts from transactions launched by Deepbit.
This seems to apply to all transactions

That time it’s not SegWit. It’s not even Pay to Script since they didn’t exists at that time (and it’s about1Vaddresses). How those inputs are specials, and what’s the purpose ?
Those transactions spend Pay-To-Pubkey outputs. These are not special or strange and are actually the very first kind of outputs to ever exist in Bitcoin. These outputs simply do not have an associated address type which is why block explorers do not show an address for them.

Also, just because a block explorer can't show an address type does not mean that Bitcoin Core can't parse it. Block explorers don't just use Bitcoin Core, and Bitcoin Core actually does not display addresses for inputs.