The adjectives smart and astute both describe intelligence, which takes many different forms! Smart usually implies a quick or ready mind; astute connotes robust comprehension, marked by piercing insight and impressive discernment of detail. When used to describe people, astute also suggests shrewdness, cleverness, and cunning. Someone who is described as astute, such as an astute politician, is able to not only understand a highly nuanced situation in great detail, but also use that insight to their advantage.
A situation is a condition or set of circumstances. A particularly unfavorable or unfortunate situation is a plight. While you will sometimes encounter plight used laughingly to describe circumstances that are exceedingly manageable—lacking clean socks, he found himself in a terrible plight—you will more commonly see plight used to discuss truly dire and precarious circumstances, as those faced by workers in perilous conditions, or refugees fleeing home for reasons of personal safety.
To allow is to permit or acknowledge something, the way a teacher might allow a student to be absent, or an insurance company might allow a claim. While not necessarily an enthusiastic show of support, allow implies no effort to hinder something from occurring. Acquiesce, on the other hand, is full of reluctance. To acquiesce is to assent tacitly, or to submit or comply silently or without protest. Typically when a person acquiesces to or in something, they're not thrilled about it, but after objection, debate, or negotiation, they're accepting it with a degree of resignation.