1- Are the trades on exchanges (from a buyer to a seller) made through the blockchain or is it virtual (exchanges only have one main wallet and virtually credit/debit the different accounts) ?
I am confused because for as I see it, transactions made on exchanges are usually credited instantly and the fees taken seem to only represent the exchange fees (not the miners fees) but at the same time, each user have several personal addresses to send the different coins.
On centralized exchanges like Bitfinex, Bitmex or Coinbase, there is no blockchain involved. They use a database and an order matching engine to execute trades between accounts. The blockchain is only involved when customers make deposits and withdrawals from the exchange.
On decentralized exchanges like IDEX or Etherdelta, trades are executed through smart contracts on the blockchain.
2- If my first assumption is correct, is coimarketcap giving volumes adjusted (volumes on all exchanges + volumes through the blockchain) ?
The exchanges voluntarily report their trading volumes, same as price data. Coimarketcap just aggregates and publishes that self-reported data.