It took me few hours thinking of the solutions, went thru and redo few versions of my solutions. But I don't think there is definite solution to this.
Solution.
Considered the facts that: 2 people are lying while the other one is telling the truth, known one of them is murderer, the person whom lies does not make him a murderer and the order of statement is irrelevant.
Considered the case where 1st suspect is telling the truth, then 2nd and 3rd are lying. This matched the facts, letting 2nd and 3rd suspects are possible killer.
Considered the case where 2nd suspect is telling the truth, then 3rd suspect is the killer and he is lying. But 1st suspect is not killer and he is telling the truth, then this does not match the required condition where "2 people are lying". This concludes that 2nd suspect can't be telling the truth.
Considered the case where 3rd suspect is telling the truth, then 1st suspect is the murderer and he is lying, and also 2nd suspect is lying eventhough he is innocent. This matched the condition.
To answer the first question.
If police is already known who is the killer after the statements, then only the case where 3rd suspect is telling the truth give the best match. This means 1st suspect is the murderer.
The case where 1st suspect is telling the truth does not give definite answer of who is murderer, only possible murderer, so it is out.
But in the case where police known one of them is the murderer, but not sure who, then the answer to the question is 1st suspect is telling the truth or 3rd is telling the truth.
To answer 2nd question.
In the case considered that only 3rd suspect is telling the truth, then 100% 1st suspect is the murderer.
In the case considered that 1st suspect is telling truth or 3rd suspect is telling the truth, then probability of murderer is 1st suspect has 50%, 2nd suspect has 25% and 3rd suspect has 25%.
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