You are so technical and it isn't good for ordinary people.
But i can't run a full node. Also i don't understand how a full node can detect a fake transaction before confirmations.
Confirmations=/ Verification of transactions.
The mining process isn't all about verifying the validity of a transaction. The transaction is verified when a full node receives it. If it meets the criterion of a valid transaction, it is included in the mempool. If its in your mempool and your node is the reference implementation, then other nodes running the same client will also see it as valid. Hence, if you can see it in your own full node, then you can be sure it is valid.
The only reason why it is appearing on Blockchain.info is because Blockchain.info runs buggy software and they don't even validate the signatures when you use their broadcast too in the past.
Double-spend isn't big problem here.
I can detect it by checking final balance and last transactions of sender address that all it's transactions are confirmed.
No. The transaction itself has to be confirmed, else it is easy to double spend it.
I don't understand it. all BTC transactions after 1st aguest 2017 are Segwit, aren't?
No. The only thing that happened then was the Bitcoin Cash fork. Segwit wasn't activated yet. Even so, not all transactions are Segwit.
I do services and get BTC from people for it. I can't wait 5 days for confirmations. Bitcoin is not user-friendly any more. I think I should choose another coin very soon
You won't have to, if you pay a decent fee.