Probably repeating some things here but....
Bolus the patient. Just do it. If their heart rate is up, if they look a little dry, even if they have a fever and that "explains" the tachycardia, just bolus them. I was scared for some reason to bolus patients as an intern-it was as if it meant they were extra sick and I would try to hold off, and I've noticed the same hesitancy in interns watching them as an upper level. (20mL/kg, unless they are a cardiac patient, a renal patient, or have a fluid overloaded status at baseline. Then as someone for more advice).
Never put anything into an orifice of a neutropenic patient. That means no rectal meds, no enemas. And always check a febrile neutropenic patient for rectal fissures.
Talk to all the nurses at start of your shift. Make mini-rounds, ask if they have anyone they are worried about, ask in advance if you can clean up any orders for them. You will save yourself several calls overnight, they will put a face on the name they are calling, and you will know who to worry about.
Call your upper level. Don't be a hero. If you have a question we want to know about it. If you are worried about someone we want to know about it. If you need help with an order we want to know about. You are our reason for being there overnight. Take advantage. And don't apologize when you call, that always feels silly.
Check on patients in person. I cannot stress enough how important this is, especially as an intern. It's very easy to just put in the order the nurse wants, or the easy answer, but if you are giving a new drug for the first time, if it's a new complaint, a new fever, pain, go get a story yourself and do an exam. In time you will learn when it's okay just to do something over the phone, but even now I almost always go see the patient.
Refusing vitals is a big deal. One of the main reasons patients are in the hospital and not at home is so we can follow their vital signs. We all want our patients to sleep overnight, but if you get called that a parent is refusing vitals, it's essential to talk to the parent and find out why and if there is a way we can better schedule vitals for them. Kids can get very sick (especially non or pre-verbal kids) without anyone knowing and they can even die, and no one would notice that their vitals are changing drastically if they aren't being taken.
Make sure every parent gets an update every day. This is especially easy to forget in places like the NICU where parents may visit infrequently. Make it your priority to call them and tell them the plan for the day. If a parent missed rounds, have the nurses call you when they get back to the room. This will save you calls and confusion, will save the night resident covering your patient the awkward conversation about a plan they don't really know, and would be what you would want if your kid was in the hospital.
Write cross cover notes. If you order a new med, if you go to the bedside to evaluate a patient, if you have a conversation with a parent, if you change a plan, write a note. No one will know about it unless you document it. It takes 5 seconds. it doesn't need to be exciting or formal. Just write it down.