Here's one to chew on: it's explained that the Soviet Union needs the US mostly intact, because of food shortages in their own territory, so it makes no sense to make the United States into a charred wasteland. But the US forces are under no such restriction. Now apparently the Soviets got most of our land based silosnote Which on its own makes no sense either since those silos would have launched as soon as the inbound missiles were detected but last I checked, in 1985 the US had a pretty large submarine force, most of which is armed with nukes. One would think the first order of the day would have been, waste Moscow, and any other major Soviet city, and probably some Mexican and Cuban cities as well. The first reasonable explanation is of course the war in the movie would have lasted a few weeks or even more likely hours when the invaders learned that their homelands were all charred wastelands and any hope of supplies or support had burned with them and either decide to go on a suicide attack or surrender. However, there is a perfectly possible explanation for the lack of a US nuclear retaliation. The United States government was unwilling to order a genocidal attack even when faced with a war which would end with many civilian and military deaths and would rather risk losing and suffer the casualties for waging a conventional war then be responsible for killing billions and causing all kinds of ecological disasters. Also, the lack of a US nuclear retaliation might help shift world opinion in their favor, causing other countries to give at least some support to the US cause if not outright join in the war effort on their side.
On top of that, the invasion is stated to have started with decapitation strikes on American command and control centers committed by infiltrators. By the time the American command chain had been reestablished, it was too late to launch nukes without risking retaliation and they likely didn't want to risk escalating the war further.
The Attempted Rape of Toni and Erica is firmly established in a line of dialogue from their grandfather, who says the Soviets "tried to have their way" with them. What's never firmly established is whether they actually succeeded with either girl. Erica's freak-out at one of the boys' crude comments (suggesting anal rape) suggests that they might have. Alternatively, however, or maybe in addition, Erica might have another source for her trauma: we're never told exactly how the girls ultimately escaped their rapists and found their way to their grandfather's place in one piece. Considering that rapists often use weapons to threaten their victims into submitting and then murder their victims when the deed is done, it may well be that Erica managed to grab her attacker's weapon and splatter him with it. This by itself would be very traumatic: as police who've ever been forced to kill someone can tell you, even if it's obviously in self-defense and there's no question that the one you killed deserved to die, killing someone is extremely traumatic. Police generally get some time off and are offered counseling whenever they do kill someone, and they're trained for this eventuality. Erica is a young girl and obviously hadn't been trained to kill. Her flip-out also might be an echo of how she managed to overpower her rapist the first time: "I killed a guy for that before, and I'll do it again!"