You've just taught me some English. The first two phrases I've never heard before, and I can't even imagine how to translate the second one.
"To break character" — "выйти из роли", "выйти из образа". E.g.: "Увидев слезы на ее глазах, он потерял концентрацию и на минуту вышел из роли злодея" Often used in positive context when an actor breaks the expected rules and interprets the character in a new way. If you would like to stress that it happened unwillingly, you can say "выпасть из роли, из образа". Another word is "расколоться". It's a colloquial expression, analogous to the English theatrical slang "to corpse".
"To suspend disbelief" — Russian Wikepedia includes an article called
'Приостановка недоверия'. I never heard this expression before and it looks really awkward, but the article mentions some alternative expressions used in literature. For example, the translation of Coleridge's Biographia Literaria, where this expression was used for the first time, speaks about "временный отказ от недоверия". In my opinion, a better translation would be "подавить недоверие" or "подавить сомнения". One might also use a figurative expression "закрыть глаза на что-либо".
I'll take a break to find a suitable translation for the second phrase.