Though all of this has really likely already been stated here, the problem with understanding these differing settings for the Windows firewall are related more to the particular words used as choices, since to most the idea of a 'Private' network sounds inherently more secure than 'Public', when in fact the reverse is really true if you examine them closely.
Instead, I'll describe how as a past network administrator and security professional, I have configured my own firewall selections since Microsoft first made theirs available in Windows XP, though I'll use the more modern Private/Public terminology in order to clarify which current Windows 10 or 11 settings apply.
When Microsoft first added the firewall to Windows XP Service Pack 2 as I recall, it quickly became popular for those with high security concerns to configure a firewall mode that blocked all inbound traffic for use when operating in unsafe environments like airports, hotels, or other external situations where the risk of direct attack of your device is typically higher, and in most cases you wouldn't be using features like file or printer sharing, since those devices are typically left at home and thus unavailable. In the Windows XP days, this all ports blocked configuration was commonly referred to as 'stealth' in popular nomenclature, since to the external networks world the PC configured this was basically invisible, since it wouldn't accept and so would also never reply to any inbound request for any service.
When creating later versions of the Windows firewall, Microsoft began using the Public network terminology to describe this mode, since they thought it was obvious that 'Public' referred to networks where the usage pattern was by the public at large, while the 'Private' term applied to networks where the usage pattern was private to individuals with physical access, such as in the home or a business.
Since the 'Public' term applies to external and untrusted networks, the legacy 'stealth' terminology relates to this type of untrusted network, so by implication, there's typically no inbound access allowed to the device in this mode, making it inherently the most secure as well as easiest to configure.
From these slightly different descriptions, you can probably guess that as a networking professional, my own devices have always been configured for the historical stealth or modern Public mode of operation, since I often traveled between both my own personal home, customer business, and less trusted networks like airport or hotels on the same day. Spending time configuring my laptop device to adjust to a particular network made little sense, since in most cases I had no need to connect directly to either the servers or printers at a customer or other non-home site, so the more important factor was to make my own device as impenetrable as possible, in case some other system on that network might have malware that could attack mine and cause me to carry it into another customer network or to my own home.
In fact, the very configuration of network sharing in order to perform either printing or in fact most modern web-based apps like email, online banking, shopping or others is really unnecessary, since these apps and devices are typically only accessed outbound from your device, with only the scanning functions of some printers requiring inbound access to your own PC/Laptop device, and even that has changed in most cases with modern printer design that takes this into account.
To this day, the Microsoft Surface Go tablet device with Windows 10 in S Mode I'm using to write this is configured for a Public network, with the HP printer fully functional including scanner, though I have no file sharing since the rare file I need is typically available to me either via my Microsoft OneDrive or directly from another external service like my bank, tax preparation, energy company or any other Internet service available online. I've purposefully operated in this manner for decades now in order to ensure this is true, avoiding not only the risk for direct attack of my personal device(s) but also the loss of data from either theft, damage, or failure of any personal device, since all of my data is stored and/or synced elsewhere.
So, unless you need to store and share data between personal devices while in the home like maybe large videos or others you'd prefer not to store externally for whatever reason, including potential temporary loss of access when your Internet is down, this mode of operation can work both to make you more resilient to individual device failure, as well as the potential loss of your home itself due to disaster, since all data is stored or synced elsewhere.
Returning to your original questions, I think this at least indirectly answers all of them, since by isolating each device from the others, you both reduce the chance of any direct attack, while still allowing access to most common devices like printers and even most modern scanners. There are likely other settings you can make to perform something similar with those various checkboxes you mentioned, but I personally prefer the most simple and straightforward configuration of Public, since I know what that means and would have to take significant steps to make it less secure, if that's even possible.
In general, I prefer to live by the 'KISS' principal; 'Keep It Simple Stupid', since this method reduces the chance that something I do might make my device less secure and also that any likely changes by Microsoft to Windows itself might do the same.
Rob