The rule is that the elements of a coordination must be parallel. They have to do the same job in the same way. All of your examples follow this rule:
{They were pleased with their lives} and {they were sure of their future}.
{They will leave big cities} and {they will live in the countryside}.
These are coordinate independent clauses. Each clause can stand on its own, and each pair can stand together.
They {were pleased with their lives} and {were sure of their future}.
They {will leave big cities} and {will live in the countryside}.
These are coordinate predicates. Each of the predicates works with this subject, so the coordination does as well.
They were {pleased with their lives} and {sure of their future}.
These are coordinate predicative modifiers. Although one is a participial phrase and the other is an adjective phrase, they are still parallel enough to work. Each of the modifiers works with the copular verb as a subject complement, so the coordination does as well.
They will {leave big cities} and {live in the countryside}
These are coordinate bare infinitive phrases. Each works as the argument of the verb "will", so the coordination works.
Things fail when the intended coordinate elements are not sufficiently parallel:
John {had a cold} and {had to call in sick}.
Two complete predicates that can each work with the given subject. This coordination is good.
* John had {a cold} and {to call in sick}.
This coordination fails. These are two different kinds of arguments, with two different relationships to the verb "had". The first wants to use "had" with its possessive sense. The second wants to use "had" in its obligatory sense. Since these two arguments don't attach to the verb in the same way, the coordination fails to attach correctly.
