Yes, unless the university is need-blind as explained below
Not necessarily. When a school is need-blind for internationals, everyone and his brother applies. The numerator (accepted internationals) never increases, but the denominator (international applicants) goes through the roof. So the MIT international acceptance rate is roughly 25% of the total rate.
Since state schools like UCLA (and some privates like CMU) don’t give international aid, not applying for aid isn’t an advantage.
And Penn’s M&T acceptance rate is microscopic, but if rejected, you may be offered a spot in SEAS.