Why can searching not lead to oneness?
Both search and not searching are both oneness. Oneness includes everything, otherwise it wouldn't be oneness. So, no matter what happens, or what you apprarently do, it's all oneness in action
What about practising to achieve enlightenment - is that possible?
Enlightenment cannot be an experience or state of mind to be gain, as it would be lost again. I think enlightenment just means understanding - but then again, that's just the thought that popped into my mind. How do I know? How does anyone know?
How can I get peace of mind
Whether your mind is at peace or not is not your choice. You don't control thoughts ultimately. Seeing this, you may let go of judging your thoughts. This may lead to a sense of peace, but there's no control in the situation - just an imagined control. So, there is no future peace of mind, there is only now. How's your mind now is all there is.