Ok first, continuer can either take "de" or "à", it's the same thing :
Je continue à t'aimer=je continue de t'aimer.
Continuer de is just more sophisticated than continuer à, that's the only difference.
Je ne suis pas là pour être aimé means I'm not here to be loved.
Je ne suis pas là d'être aimé means I'm not here for being loved, but we wouldn't say it like that except for poetry. We would rather say "je ne suis pas là parce que je suis aimé".
"pour" before a verb means "to" in a meaning of "in order to". "de" means "to" also, but just as a link word.
Je ne suis pas là pour parler=I'm not here in order to speak.
Il est inutile de parler=It's useless to speak.
So when you can replace "to" by "in order to", you use "pour". If you can't, you use "de".
This is just a simple way to make you understand, but things are more complicated when it comes to the grammar of a language. As you can see with "continuer", sometimes, the idiom takes "de" or "à" or "pour", because that's just the way it is, just like in English (i want TO, to talk TO, to go TO, to come FROM...), you have to learn it by heart.
Plus, "de"/"pour"/"à" can translate other English words, depending on the context.
About "c'est" and "il est", I'm not sure to understand your question, as "c'est" or "il est" are usually not immediately followed by a verb, except for idioms such as "c'est à dire", 'il est à noter", and it would be "à", not "de".