when to make a liason between words spoken

Hi Michael, 

First just to say that there are three types of liaisons in French -

Mandatory liaisons: liaisons every French person will pronounce

Forbidden liaisons: these are liaisons which would never be said by a French native (but might be tempting)

Optional liaisons: some liaisons depend on social background, age, mood, and tradition. In this section ‘over liaising’ can sound precious.

Your first two examples - come under 'optional' as you will hear both in France 

Your third example has two liaisons which are mandatory

Ils (z) étaient ( because otherwise, you would hear the singular 'il était')

In fact, after the personal pronouns nous, vous, ils, and elles,  you will liaise the last -s with a following verb starting with a vowel or an h- mute.

i.e.

 elles (z) ont, vous (z) avez, ils (z) habitent  etc...

In the case of meilleurs amis, again you would make it to mark the plural.

Here is a sentence that has many liaisons -

Les artistes sont arrivés chez eux en avance -----> Les (z) artistes sont (t) arrivés chez (z) eux en (n) avance ( The artists arrived home early) 

All are mandatory apart from sont arrivés which can be pronounced -

sont// arrivés or sont (t) arrivés

This is a vast and complicated subject that involves lots of different cases and is in the pipeline but hope this helps!