Hello, I am Nehal.
I am trying to understand the idea of BOINC and how it works. I have a question regarding the adding a new project on BOINC.
Can anyone create a BOINC project? Or Is there a way to register your project on BOINC to be able to use the computing power of the volunteers?
Is there any way to verify and stop anyone from deploying malicious projects on the BOINC volunteer's machine?

Is there any way to verify and stop anyone from deploying malicious projects on the BOINC volunteer's machine?

The permissions with which tasks run under Linux and other unix based systems provides some protection.

Yes.
Unless you are using a third party manager or science united you can have to select and join each project you want to run, and this has to be done on each computer.
The situation is a bit more confusing when it comes to the third party managers, with some you can select the projects you want to join, and the manager does all the configuration etc. Science united is a bit of a loose cannon - you decide the topic you want to run (e.g. biology, medical science etc.) and science united will decide which projects your computers will join.
Obviously when you have control over the projects you join you have a high degree of control, and most (all?) the projects on the BOINC list may be considered "safe". Likewise with the third party managers the majority of the projects available are drawn from the BOINC list, but some may come from other sources. Science united should be OK as a manger, but it does tend to pick some rather random projects which may not be to you liking.
As for those projects not on the BOINC list - "buyer beware".