1)A: The problem is that the regulations don't allow us to use next year's budget.
B: Don't worry. We'll get by / get around it somehow.
Are the two verbs in bold possibile? Do they mean the same in this context?
"Get around" and "get by" are both phrasal verbs. Look here: English Phrasal Verbs - UsingEnglish.com
"Get around" means they will use next year's budget anyway; but find some accounting trick, deceitful explanation, or other subterfuge to do what they want to do regardless of the "rule."
"Get by" means that they will survive, persevere while obeying the rule.