This is an informal question-cum-request. In business meetings i can envisage its usage only for finding a way to accommodate oneself - Ничего, если я сяду здесь? Ничего, если я положу сюда свою сумку? and the like - that is for things not directly related to the objectives of the meeting, unless one is on friendly terms with the opposite party.
However with requests for significant favors it may come off as a little presumptuous and insolent, because it's basically an expression of a decision made in advance for which only a formal consent is being sought, it expects a positive response before considering the other party's opinion. It's as if one would ask You don't mind me living here for a while, right/do you?
Besides your variant, a positive response could be Да, без проблем or (Да) Без проблем / (Да) Пожалуйста / (Да) Ради бога / (Да) Живи сколько хочешь / Живи (less welcoming) / Ну ладно (, живи) / Ну живи (still less welcoming). Да being an enthusiastic particle.