This girl has potential, but this song was not that good.
Here are some tips:
1) Being off tune really takes away from a performance. If you are off tune, your song will not sound good. You can take voice lessons, or just practice singing along with CDs or a piano.
2) Her voice sounded strained a lot of the song. Singing often, drinking water to keep your vocal chords hydrated, and doing vocal warm ups can help with this problem. It is impossible to train your vocal chords to be looser (and sing lower) but you can train them to vibrate faster and sing higher. Practice singing a little higher than normal to improve your range. Never strain your voice, though.
3) In a lot of the song, her voice had a nasaly sound. While this is popular for pop singing, it doesn't actually sound that good. Put your finger on the top of your mouth just behind your teeth. It will feel hard. Now move your finger furthur back…it will feel softer. They are called your hard and soft pallets. When you are singing, you should lift up your soft pallet in the back to get a more mature, open sound. Now yawn. You can feel your soft pallet going up. Aim for a little more of that when you sing.
3) Take away some of the acting. It was actually distracting, and probably made her singing worse!

No matter what, she should keep singing.

Singing very hard songs isn't a good way to improve. A contralto will find difficult songs for sopranos impossible to sing and a soprano will have the same problem with difficult contralto songs. However, singing easy songs for a different vocal type isn't that harmful, especially if singing them is comfortable. Imagine a contralto trying to sing the queen of the night (an extremely hard soprano aria which most sopranos can't sing), she will damage her voice for sure. You should sing anything that is comfortable and easy and you will improve. Then move to something a bit harder. Don't start with something very hard. Hard songs will become easy for you eventually. I'm sure you don't want to damage your voice.
Sorry for my bad english, I hope I helped you =)

Most of the time, guys can only sing higher than girls when they haven't matured quite yet. However, I am in choir and I do know a certain baritone who can sing high by using head voice. But if you match the same pitch, you'll notice that girls are sometimes higher. A girl's voice is naturally an octave higher than a boys. To answer, your question, yes, some guys can sing higher than girls. When you get the chance, check out Adam Lambert and listen to his voice. You'll notice that some notes he hits are higher than altos most of the time, a male soprano.