Learn English – Are”the name of the brother’s friend’s father is John’ or ‘My brother’s friend’s father’s name is John’ grammatical

So let's start with the singular 'brother-in-law', which is perfectly clear. If you have a single brother-in-law and he possesses something, this is written as:

My brother-in-law's cooking skills are excellent.

If you have more than one brother-in-law (no possession) you would write:

My brothers-in-law are all brunettes.

This is because when pluralizing a compound noun, we always add the 's' to the most 'important' word. The fact that they are brothers is most important, so it gets the 's'. This is the same for "mothers-in-law", "fathers-in-law", etc.

If you have more than one brother-in-law and they all own something:

My brothers-in-law's restaurant is the best in town!

Confirmation of this final construction can be found at grammarbook.com:

Rule 7

If the compound noun is plural, form the plural first and then use the apostrophe.

Example: my two brothers-in-law's hats

1. We speak of possessive or genitive only when a noun (or noun phrase) is marked with the 's clitic (or with a bare apostrophe if the noun or noun phrase ends with ‹s› or ‹z›).

   None of your examples employs this marker, so all of them are what grammarians call attributive nouns: nouns which act like adjectives 'modifying' a following noun.

   (Some writers on grammar also call constructions with of preposition phrases, like NOUN of NOUN, 'genitive'; but that is not relevant here.)

2. The term possessive is a grammatical term, not a semantic one—that is, not a term which indicates actual "possession". There are other relationships which the possessive may signify. For instance, when the second noun, the one which is not possessive, is derived from a verb, the noun in the possessive case may be the agent, the semantic subject of the action which the second noun designates:

   Columbus' discovery of America ← Columbus discovered America

   In other cases the possessive may mark the patient, the semantic object of the action:

   Germany's defeat by the Allies → Germany was defeated by the Allies

3. Attributive nouns have an even wider range of reference. A bicycle rider is someone who rides a bicycle, a bicycle store is a store where bicycles are sold, a bicycle tire is a tire for a bicycle, a bicycle race is a race in which the competitors ride bicycles. In your examples:

   • Syllabus highlights are the main points in a syllabus
   • Relationship problems are problems with or concerning a relationship
   • Admission requirements are what is required of those who apply for admission