I will only address the main grounds and not the smaller issues.
As I understand the main arguments, technically speaking the invasion is legal on two grounds and illegal on two grounds;
Legal
Existing UN Resolutions; Hussein's refusal to co-operate with the AEC was a 'trigger- point' for military action under the resolutions.
Human Rights Treaty; this is the more tricky one; as discussed in a previous thread, in order to be in violation of the Treaty, Iraq had to 'dob' themselves in- which they obviously weren't going to do. but the Treaty does allow for the removal of a 'genocidal' government.

Illegal
UN Charter; specifically rules out invasions without UN approval (Security Council) which the US/UK/Aus/Spain/Poland did not seek since this undermined their argument as to pre-existing resolutions giving them the authority they required.
Human Rights Treaty; Yes! it makes it illegal too. which is one of the major criticisms of the Treaty. Under the second Treaty (Hague Accords? Sorry, going from memory), the invasion is specifically ruled out because it has to be approved by the UN as well as being 'okay' under the Treaty.

An additional factor is that it could be argued that there is a precedent (legally) for the Alliance action; the Viet Namese invasion of Cambodia.

Under the Westminster System, Parliament can not be a court. I could be wrong in my interpretation of what would happen, but under Parliamentary Privilege a member of Parliament can not be prosecuted for what is said in Parliament. If, however, Parliament decides (by two thirds majority of both houses) that you have lied TO Parliament, then that Privilege is removed and you are then liable for prosecution. Parliament can recommend charges through special hearings or by convening a Royal Commision, but it can't empanel itself as a court.

The problem with the deal between the US/UK on matters of Intelligence and Technology exchanges is that, by definition, much of the exchange is of classified material. The Australian deal is not so good as the UK deal and I have not heard one person who has a good idea of what it involves for us say it is not worth it. But then we didn't lose 200soldiers either. I suppose it depends on whether you're more 'interested' in the big picture or the smaller picture. (I could probably put that better but everything else i thought of sounded worse- it's not meant as a criticism).