Let's say I want to make a large transfer to an exchange. I am sure to verify the receiver address. However, if the exchange made a mistake somehow, all the bitcoin would be lost forever. So does it make sense to send a small amount first, confirm that they receive it, and then send the rest?
Because I have also heard that each address should not be used more than once.
If you know how, I'd recommend signing all the funds over first, storing the transaction offline and broadcasting a smaller one. If you get an email confirming your pending deposit before you've got a confirmation you may also be able to double spend the original transaction allowing for you to mitigate paying extra fees (as the 2 transactions could be replaced by one).
This assumes you're sending your entire wallet as it'll probably cause extra hassle if you don't (also if you're not confident in how to do it I'd stick with sending the smaller amount first and the larger amount afterwards).