Are international (NON-EU/EEA/SCHENGEN) tourists generally required upon entering the UK at the border to provide any information at all about the person they're visiting (both in case they're staying at this person's place, or in case they're staying in a hotel) if they're coming to the UK to visit a family member or a friend?
From a legal point of view, yes, they are generally required to provide this information, but in practical terms, they are only required to provide it if the officer asks for it, and officers often do not ask. As an example, I once entered the UK on a US passport, saying that I was going to be there for a few days visiting a friend. The officer did not ask for any information about the friend.
An officer who has asked for this information may refuse entry if the refusal to provide the information leads the officer to conclude that the traveler has not shown that he or she meets the conditions that apply to the category in which he or she seeks to enter the UK (for example, as a visitor or as a student). There are questions here where people have had visas refused because of inadequate information about the person they're visiting, and an immigration officer is entitled to seek the same information from someone at the border as they would be required to submit in a visa application.
In case of a positive answer to the above: is this information only provided orally, informally and off-the-records to the border agent, or will a record be kept?
It is certainly not off the record. The officer may record the information in the traveler's database record, even if it is given only orally. But it is by no means guaranteed that the officer will in fact record it.