yes, you got it right.
I’ve recompiled restoring the line of code 3.0.1 above and copied this compiled dll in HCC 3.1.0 installation and these two bugs go away.
The reason I think it is because the MVC routing are registered without culture locale in the URL and this do not match with that. If this last pull has reason to be maintained then to make it work fine it is also necessary to update the mvc API routes with culture locale.

I've pinged the developer behind those updates. Hopefully, they'll reply directly here. If not, I'll relay their reply here for them.

I was able to get ahold of the developer that made these updates that we're speaking about. Unfortunately, they're not allowed to participate in these forums. So I'll do my best to relay the information by proxy.

The update you're referring to and reverted was necessary to support child portal URL's and use cases when the primary URL was not properly marked in the database. It was also a necessary update to support 8.xx of DNN because the original code would always be a blank URL if left as-is.

Can you try to roll back your core code change and ensure that you have a primary URL has been set in the database? Also, what version of DNN are you on?

Sure, I've rollback my code and checked if I've a primary URL:
[img=http://95.110.156.198/ForumImages/SiteAliases.jpg]Site Alias Settings[/img]
I've also tried to leave only one primary URL (for only www.hotcakes.it) and nothing change. I've also checked the DB and the same is there.
About the DNN version, I've downloaded the Github core version with DNN Platform 8.0.3, however you can find the full work website in a zip file [url=http://95.110.156.198/ForumImages/Website.zip]here[/url], to make it work you need only to add on host file the line and add it on IIS (user:host passw:1234567)
Alternatively to replicate the issue in your HCC 3.1.0 installation you only need to enable multilanguage as shown below:
[img=http://95.110.156.198/ForumImages/MultilanguageEnabled.jpg]Multilanguage Enabled[/img]

a thought:
I'm really grateful for your proxy function but it gives rise to some doubts in me...I do not understand the reason why they are not allowed to this forum but in the past years I have hardly paid the choice to use products supported by only one person and when I found hotcakes it seemed like a solution to the past...I do not know if I was able to explain myself with my bad English

The person that isn't allowed to participate in the forums doesn't work for my organization. I'm unable to speak to why they might not be allowed to post in the forums. I have other concerns around that myself.

As for downloading and troubleshooting a copy of your website, that's very much outside of the scope of support that I'll be able to provide in the community forums. Something that takes that much time is reserved for our supported clients. I know this isn't a convenient or desired response, and I apologize for that.