Hey! The direct translation would be “위대한 사람들은 같은 생각을 한다”, but we don’t use this phrase in Korean and it just sounds a lil awkward. A more natural way of saying this would be something like “너도 나랑 같은 생각을 했구나!” Which roughly translates to “oh, you’ve thought of the same thing as me!” Hope this helped!

Hey! Generally, we wouldn't use "먄하다" instead of '미안하다'

Hi! I think "He accepted the invitation and is looking forward to the visit." sounds the most natural. Hope this helped!

Hey! So the whole sentence means something along the lines of "the reason for the continued increase of educational expenses in household expenditure even amidst an economic depression, can be seen as the passion for education that parents have, which leads to them trying not to cut down on educational expenses for their children, even if it means not eating and not spending (on other 'things')." So the '안 먹고 안 쓰더라도' part roughly translates to "even if they don't eat and spend (money on other things)" and the '으려는' part is something like "trying to" so in this case, it means "trying not to cut down on (educational expenses)". I'm sorry if this isn't clear, but feel free to ask if you don't understand!