i used a big unnamed provider to transfer my funds from a hardware wallet to online but with a loss of 7% while the overview page promised a low fee. they said there were some discrepency in my transaction and offer me 50usd, but that is WAY to low...
The price is irrelevant. When you send bitcoins from one address to another, you still have the same amount of bitcoins, less the transaction fee.
Did you sell the bitcoins after transferring them? Is that the 7% drop?
As for the data you are looking for, the exchange should have price data including the low and high prices for the period. That should be sufficient. You don't necessarily need the price of every trade.