When opening the rubbish chute, there is always a disgusting smell. Is there any way to remove it such that when I open to throw my rubbish, I will not smell it?
To some degree, your garbage chute is always going to smell a bit like garbage. There are however some things simple and complex you can do to reduce it.
First, you need to clean it and ensure that any stuck food/grime is dislodged. Give it a hose-down (pressure washer if you can) and then disinfect/deodourize it. If there is crap stuck in there, it doesn't matter what else you do, it will keep smelling.
Make sure that whatever you throw down it is in a sealed bag; do not throw loose scraps down.
If it doesn't already have one, a flap on the opening will help keep some of the smell down - usually you have to push you garbage through it and then it springs back closed.
If you can control it, empty the garbage bin at the bottom frequently so food does not sit down there rotting (and smelling for ages).
As a commenter mentioned, positive pressure in the room will keep the smell from leaking into the room. Condo's use this mainly for fire prevention but it also helps keep smells at bay (or in the originating condo at least). A fan alone will not create the pressure, you need to be bringing in outside air at a faster rate then it escapes so that there is always positive pressure.