'Ego' is the word that we commonly use for that sense of 'I' that feels limited in all of the myriad ways we are familiar with, from 'I am a body that will die' to 'I am afraid of the dark'. This ego does not really exist.
'Self' is the term used by Advaita for that which is the only real thing there is. Before moving on, it is necessary to qualify this by saying that it is not a 'thing' in the way we usually use this word. Obviously, if it is the ONLY thing, then it cannot be an object in the sense of 'observer-act of observing-observed'. Indeed, we cannot really talk about it at all. It is simply not amenable to thinking about (since to be able to do so, it would have to be objectifiable in terms of concepts and we have just said that it isn't).
So, you ask "Who is limiting itself?" Sorry! - again, confusion of terms. It is the (non-existent) ego that appears to be limited. The Self is without limiting properties. The ego arises in the first instance by virtue of the mis-identification of the Self with something in creation. The body is seen - the thought arises: 'I am this body' - I feel limited by this body (e.g. I have sprained my ankle and cannot walk etc.). Why does this happen? Because of ignorance. I do not realise that I am the unlimited Self (see adhyaasa). It is important to realise that the Self never actually becomes limited.
There is an analogy for this, courtesy of Swami Parthasarathy. Imagine a piece of iron, say the hinge of a door. If you bring a magnet close to the iron, the iron will be attracted and stick to the magnet. Now detach the iron, take a thin piece of wood and bring it close to the magnet. There is no attraction. But, if you take some string or an elastic band and attach the hinge to the wood and then bring the magnet close to the wood, assuming it is a sufficiently powerful magnet, the wood will be attracted to it and stick. Note that it is only by virtue of its attachment to the iron that the wood appears to be attracted to the magnet. In reality, the wood 'has nothing to do with' the magnet.
In an analogous manner, the Self has 'nothing to do with' the world - is totally unaffected by it. What happens, though, is that the Self becomes identified with something in creation and that 'something' IS bound by the laws of creation. Thus it seems as if our real Self is bound, subject to misery and death and all the rest of the apparent vicissitudes.
The 'answer' is not found, however, by any of this intellectualising (interesting though it is!). Indeed, while we continue seeking, we are doomed not to find the answer. It must be the ultimate Catch 22 situation. All of the problems that we are trying to solve belong to the ego, the person, not to the Self. The person can never become enlightened and the Self already is pure light. Our desire to become the Self is a denial of the fact that we already are. We have to get rid of the desire for freedom before we can appreciate that we are already free.
This is what is meant by the Mulla Nasruddin story where he is looking under the lamp for a lost key. He explains that he didn't actually lose it there but it's the only place with sufficient light to look for anything. We continue looking everywhere but within because our minds and intellect are only able to cope with things 'out there'. There is also the story of the man looking everywhere for his spectacles when they are pushed up onto his forehead all of the time.
Our true nature is beyond mind and body and can never be found by asking questions, the answers to which are ultimately satisfying only to the intellect and solve nothing. It is, after all, the ego that is asking the questions and the ego can never become enlightened - it doesn't really exist! Only when this is understood and accepted absolutely does full realisation of the truth become possible.