Most importantly, have fun playing with your son!
For your question, in case there is no second most common Action card in a player's deck, that number would be 0. Or maybe it's non-existent, but you certainly don't count the most common one (that's kind of the strategic point of the card). So your son should have gotten 0 VP from Triumphal Arch in that ...
As of 2019, there are 13 sets and 11 promo cards1; with another set announced as coming sometime early 2020.
In release order:
Dominion (Base game)
And the list of Promo cards:
Envoy (November 2008)
Black Market (March 2009)
Stash (February ...
In Dominion, you can play a card instructing you to do something impossible; you just fail to do it and the game continues. So yes, you absolutely can.
More generally, you don't need to anticipate every game state that might happen if you play a card...in many cases, this is impossible anyway. You just need to follow the directions of the card, and skip ...
In Dominion, the general rule is that you have to do everything on a card in order before you can play another card.
This affects Throne Room in an odd way, because it means you have to do everything printed on the card Throne Room tells you to play, then do everything on that card again.
Thus, when you Throne Room a Throne Room, you play one card and ...