Watch CSI and shows like that.
Yup, it could be mistaken as a suicide.
Yup, it can be proven that she was pushed.
How?
- there could be signs of a struggle in her room to indicate a fight
- a neighbor could have heard her screaming or arguing with someone to indicate that she was not a alone during the time of the murder
- the killer could have left some hair, fingerprints, etc.
There are lots of ways, really, to prove that it was a murder. Also, even if the crime scene first looks like a suicide, there will still be an investigation to eliminate all possibilities so the detectives/police/etc. will still be able to see the evidence of murder even if it is first presumed to be a suicide.
The amount of evidence left by the killer is all up to you.
Again, watch CSI.