Twain likely made Henry Adams an American in England to show how far removed he was from what was viewed as proper English society. As an American he would be considered a backwards outsider that could not possibly fit in. That all changes when he receives the bank-note and then can afford to buy his way into the English society.
“It is awfully hard work doing nothing”
The main idea behind it is that life is short and that we need to laugh and be happy while we have time and not focus on negative things because life is short. If life hits you in the teeth there's no reason to be depressed forever about it, just laugh and be happy and keep moving on.
