1) What BTC online blockexplorer is the best/shows the most info? Shows for example from which TXs my ammoutn came out etc.?
All block explorers will show that. I personally find
Blocktrail and
Blockcypher to be very smooth block explorers, but many users will use
blockchain.info.
2) What fee did i pay Bistamp for the BTC withdrawn...? (it was a smaller ammount of BTC) cause it almost looks like i didnt pay any fee for BTC withdrwan... I didnt see any "field" where to enter the fee i want to pay, and even the online explorers dont show any fees (if i understand them correctly) and also my bistamp balance (BTC and fiat) is lowered by only the exact ammount i withdrawn... no fee anywhere...? what is this?
Bitstamp doesn't charge fees for Bitcoin withdrawals.
However, all professional exchanges set transaction fees themselves (on the actual transaction). You must not be reading it correctly. A professional exchange like Bitstamp will most likely set fees of >200 satoshi/byte, often higher, and will have bundled up these transactions into one for efficiency.
You should look at where it mentions the satoshi/byte of the transaction. Ideally they will have set fees of >400 satoshi/byte, but anything over 200 satoshi/byte.
Post the transaction ID so that we can check.
