you'll probably take the I-105 to I-605 to I-10 to I-15....there are tons of Los Angeles suburbs here with tons of gas stations and restaurants, only a few will be open over night, usually diners like Norms or Dennys, but you can usually find places there. Once you get on I-15, as M4travels said, you're going to have fewer places to stop.
Victorville is one of the first place you'll hit after crossing over the San Bernardino mountains that should have several places to stop for gas, coffee, food or bathrooms (by the way, going over the mountains it's pretty steep, so stay alert for that). There are several exits for Victorville, but you can usually see the signs up ahead for what's coming a mile away (land is pretty flat since it's desert).
After that the next big place is Barstow and you should find some places there for gas and coffee and breakfast. (That's where the I-15 splits off and also connects with I-40 by the way).
After Barstow there won't be much for the next couple of hours. There are a couple of rest areas that will have bathrooms, and probably vending machines. And a few itty bitty "towns" which basically have a single gas station, but not much until you get into Nevada.
Once in Nevada, you'll see several curious "towns" which are basically casinos with a couple of gas stations and maybe, maybe a McDonalds, but the gas stations do generally have restrooms. (Primm, Jean and Sloan are the big three). And then you'll be in Vegas.
At that time of night/morning, you should be in Vegas in about 4-4 1/2 hours, five tops if there's much morning traffic on the way into Vegas.
I don't know where you are staying in Vegas, but if you're driving back to LA from there, there are several reasonably priced gas stations on Tropicana Ave. just west of the exit ramps for I-15.
Have fun, sunrise over the desert should be spectacular!!!!!!!!!!!!!!!!
Edited to add: to answer some of your other questions.... I haven't heard of I-15 being any more dangerous to drive at night than anywhere else. Keep your doors locked when you stop, and if you see anything odd, go someplace well lit. There are emergency call boxes along the road at regular intervals if you break down or have trouble, the operator on the other side of the line can get you a tow truck or the cops if you need them.
The road could possibly be very windy if we're experiencing Santa Ana winds from the east. Sometimes trucks have tipped over because the wind was strong, so be vigilant.
Also, you're not really going to miss much scenery by going at night, not a lot to see on the roads you'll be taking...except the aformentioned sunrise which could be breathtaking, otherwise, just a few deserts, mountains and such......but the stars in the sky should be super clear and brilliant at night, so going at night is actually somewhat preferable....plus less traffic....just watch your speed, I-15 is patrolled by helicopters and planes.
