but what he says is that because all the utxo are aroung 10 gb even if my bitcoin core node is pruned and don't keep every block on his disk, he will actually keep every utxo list
This is right.
Even if you run a pruned node, you have to keep the UTXO set.
and he says that once my bitcoin node would have finish syncing with the network (even in prune mode) I would be able to see the balance of any wallet (even one create before I started my bitcoin core setup, 2 days ago in my situation).
This is wrong.
If you load a new wallet.dat, you will have to redownload the blockchain, so that the transactions are displayed.
What I don't understand here is why the bitcoin blockchain size is about 900 gb but every uxto are around 10 gb, what all those block contains if it's not just utxo, here we are talking about bitcoin and not ethereum or an other blockchain where we can execute function things like that
The bitcoin blockchain includes all the transactions that have been made so far.
The UTXO set is much smaller in size, because it's just a list including some information about unspent outputs.
Each bitcoin transaction contains ID(s) of the parents along with the index of the output(s) that are spent, unlocking script(s), locking script(s), amount of output(s) and some other information that I may have forgotten to mention. All these data are recorded in the blockchain.
In UTXO set, we only have some information about unspent outputs like the ID of the transaction that has created the UTXO along with its index in the transaction, their amount and locking script.
Also note that UTXO stands for
Unspent Transaction Output. Once a UTXO is spent, it's removed from the UTXO set.