If you're too tired to lift, you shouldn't lift. Take a nap after school or go to sleep earlier. There's no reason why you should be going to sleep at 3 if you have to wake up early.
Sleep in on the weekends, go to sleep 30 minutes earlier every night and throw a few naps in every week. Then get in the weight room and don't think about anything else but getting bigger and stronger.
Vin, trust me man, it's hard to get a decent workout in (let alone function like a civil and sociable Human) when you're running on 3 or 4 hours of sleep.
If you have to lift on days that happens (which should be rare occasions, get off the Xbox kid! [joking, joking]) then definitely try to grab a 20-minute nap after school or before dinner, if you can. That'll do wonders to recharge you. Hurray for naps!!!!
Why is a senior in high school going to sleep at 1-3 in the morning? Senior year (especially second semester) is easy as shit. Your gpa is mostly already set in stone at that point. I wonder how you will make in college if high school is already wiping you out. You had better give up on the idea of grad school. Either that or sell your bed.
This is an interesting question, which, to my knowledge, has no definitive answer. Some nutrition protocols have you waking up in the middle of the night to chug a shake in order to keep growing. Of course, others say that you're doing more damage by interupting a normal 8 hour sleep cycle.
My opinion? Sleep is way UNDER-rated. There is simply no substitute for quality, consistent sleep. Sounds like you're in a situation where you're getting up in the middle of the night no matter what, so I wouldn't sweat it, as long as you're still getting a total of ~8 hours. Sure it may not be ideal, but you'll still progress. And why not feed yourself while you're up...