Don't know about having to hold ALT on boot.
Apple seems to purposely deprecate older hardware (they use the word "vintaging") which- in effect- means old hardware- even if robust and capable- will no longer get macOS updates. Apple and Apple fans will spin that this is about not having to support "outdated" hardware but patches/hacks clearly demonstrate that unpaid, third parties can make newer versions of macOS run on older hardware just fine. If uncompensated hackers can do it, it seems a very rich corporation would have plenty of resources to do it too. Why don't they? Presumably, they would rather you buy a new Mac and give them a fresh pop of new cash. Very rich corp vs. starving artist hacker.
So yes, you need patches/hacks if you want to try to get 2011 hardware working with newer versions of MacOS. Apple basically demands it or else (give them more money).
i7 vs. i5? Given what I just shared, I wouldn't spend new money on this hardware upgrade. Apple really does NOT support trying to keep vintaged hardware usable, so it would seem to be wasting money on what will be an increasingly obsolete platform. Apple is basically working against your objectives here. You cannot "keep up" with macOS by compatible hardware upgrades (presumably because Apple doesn't make enough profit from you trying). In this scenario, Apple is essentially Ferris Bueller in the last bit of video after the credits...
On a broader scale, given that Apple choices basically have left that computer behind, you might consider the OTHER option: install Windows and make it a nice PC. Microsoft's philosophy is to generally NOT leave older hardware behind and I'm confident you can install at least a full version of Windows 10 on it with no issues. Windows 10 will be kept up to date for at least a few more years, so your kids can have a full computer with up-to-date software for a few years before MAYBE Microsoft finally quits on what might be 15 year old hardware at that point (and that's only a "might"- there is plenty of history of Microsoft extending their cutoff dates).
For the kid purposes you share, Windows will likely be the better choice anyway- particularly with gaming goals.
If you are an "only Apple or bust" person, sell that computer for whatever you can get and put the money towards perhaps a refurb Mac Mini M2 or M1. It will be up-to-date and likely 5-7 years before being "vintaged." If you want to play in Apple's sandbox, you generally have to stay pretty close to "latest" and expect to regularly pay to do so. It's helped make them a very rich corporation.