Bellow I answer to each question you asked:

1. Based on what you describe, it is on a hardware wallet, probably Ledger Nano (X or S) or Trezor. Both are accompanied with a software that you can install on your pc. This software interacts with the wallet (you connect it on the usb port) and acts as a UI, it presents you all the coins you have "stored" inside.
   Technically speaking Bitcoins (and any other coins issued on the blockchain) are generated on the blockchain and "live" there forever. No one can move them. So his Bitcoin is not in his wallet. What is stored in the wallet is the private with which the Bitcoin was signed on the blockchain (public/private key cryptography is used to this end). So, the private key is the critical thing that gives you ownership on the Bitcoin. The owner of the wallet can look at the UI and find the quantity of the Bitcoin "stored" in the wallet. He will need to enter his password on the wallet.

2. The risk with a direct trade between the seller and the buyer is that whoever does his part first can not trust the other side will meet his obligation. e.g. The seller sends the Bitcoin to the buyer's Bitcoin address (it can be easily done with the wallet UI I described on (1)), but then the buyer denies to send the euros to the seller's bank account. This is the traditional trust problem, that introduced the need of a 3rd party, the "middleman" (first being the Medici family). And even if the buyer meets his obligation, then a huge amount will enter the seller's bank account. So, the seller will have trouble explaining it to the tax authorities as the result of a trading. Instead, tax authorities will probably deem it profit from working and tax him as if it was a salary. An accountant's advice is needed before someone does a direct trade.

3. Yes, an exchange is the way I would suggest. This way you can easily prove to tax authorities that this is profit from trading and you will pay capital gains tax on the net profit (sell amount in fiat - buy amount in fiat).
   Yes, the process you describe is accurate, you create an account (Binance, Coinbase, Kraken are the most prominent, I use Binance). You follow the KYC process. Then you send the Bitcoin from your hardware wallet to your Bitcoin wallet in the exchange. Then you trade the Bitcoin for Euro. Finally you send a SEPA bank account transfer from your Euro wallet in the exchange to your bank account. Regarding fees, I can only speak about UK and the same process in GBP, in this case Binance has the lowest fees. In Greece/Eurozone things might be different though, your friend needs to do his own research.

4. If you can prove the profit is from trading, you are taxed with capital gains tax on the net profit (sell amount in fiat - buy amount in fiat). Otherwise you are in trouble. You will probably be taxed on the whole amount (sell amount in fiat) and it will probably be deemed as labour, so it will be taxed as a salary. Your friend NEEDS to get professional advice from an accountant before selling, because legislation is different from country to country and again I can only be sure about the UK legislation.