If I buy and download a game through second Nintendo account do I own it on my main account too?
Solution 1:
I'm worried that the game will think it is owned by the second account and not the main one which would be a pain because I hate having multiple accounts with different games on them.
The game will definitely belong to the second account. I know this because my wife and I have two separate accounts on the same Switch. An account can be linked to multiple Switches, but only one Switch can be identified as the "primary device" for a given account.
Games bought for a given account account are:
visible in the installed games list for all accounts on the device.
playable by all accounts on the device if this is the primary device for the account that owns the game.
playable only by the account that owns the game if this is not the primary device. (And you will need an internet connection at all times.)
available to be downloaded from the eShop only by the account that bought it.
Here's some more detailed information about primary device vs non-primary device.
I wasn't able to find any information on whether parental controls would block your first (under 18) account from playing the game bought by the secondary (over 18) account. You mention a video that shows you how to do this and that it works, but I find that a surprising oversight on Nintendo's part. Be aware that even if it works today, it might get patched out tomorrow, and that would presumably lock you out of any saves for that game which you've built up on the first account.
Also, be aware that once you have multiple accounts on a single Switch, it will pop up and ask you which account you want to play with for every game on that Switch, regardless of which account owns it. Which means if your parents ever use the device themselves, they may notice a new account they don't remember creating in that list.
I believe a list of accounts associated to the device is also available through the parental controls app on iOS (and presumably Android? I have an iPhone.) I haven't played too much with that, though.
Solution 2:
If the accounts are on the same switch, yes, you can play it on your main account (on that switch) but the game will be owned to the other account although I cannot see why this would be a problem unless you owned another switch. If you were to log in on your main account on another switch, you would not be able to play doom unless another account on that switch had doom (eg. Your other account).