In most uses, on and upon are interchangeable: except in some set expressions, on is more common. There are some transferred meanings of on where you can't use upon (for example, on television, on Thursday) but others where you can (eg as a temporal conjunction on seeing him = upon seeing him).
Into always has a meaning of movement or transition. In can have ...
You need to add an "s" to your prohibit (3rd person singular).
You cannot prohibit something on someone else. But you can impose a ban on drinking alcohol (Cambridge), though I wouldn't use this strong phrase in connection with religion unless you want to criticise it.
You could maybe say
Our religion does not allow us to drink alcohol.
I'd probably phrase that as "I'm studying the log files Ben generated for bug ticket H-201."
Either "for" or "on" could work there. "After" was the preposition that moreso stood out to me as being a bit confusing. That usually indicates something which happens later than something else in chronological order, which ...
I think to me would be a more idiomatic choice here.
You will always remain a very hilarious guy to me.
To me, you will always remain a very hilarious guy.
You can use the definite article there.
You will always remain the love of my life.
Similarly, we say
Warmth and light brought joy to my heart.
"Apply for" sounds most natural. It is correct when followed by an object, such as "apply for a job."
"Apply to" is more rare, but you might hear it sometimes in situations such as an indirect object ("apply to that company"), or in an infinitive verb ("apply to transfer into the department").
"Heads of a thousand inmates were cut." is wrong.
"The heads of a thousand inmates were cut." is technically correct, but rather awkward. I would say "A thousand inmates' heads were cut. "
"The head of a thousand inmates was/were?" this is wrong, as it would need to be "heads... were" because it is plural, ...
In my opinion, none of the sentences you gave as examples are incorrect, although I generally prefer the ones you prefer. Before I would worry about the "the"s not being there, I would worry about the definitions for demand saying "number" instead of the preferable "function of" some proxy, which is still a pretty negligible ...
For of, I think that this is the most relevant meaning:
typical or characteristic of
used to show the place where someone or something starts
What you expect of somebody relates to the way they are, and the way that they behave, without reference to your involvement in that behaviour.
What you expect from somebody relates to what you personally ...