Thank you coming back to me to address your points:
1. The comparison to a dead body is not a pertinent one because there is a formal legal procedure that is needed to certify a death, there is not one for determining whether or not a picture is racist except in the instance of a criminal prosecution and presumably you would not want the matter referred to the police for a potential criminal prosecution of your son for a hate crime.
2. Any breach of the schools expulsion procedure is at best arguably a breach of contract but one which would not likely result in your son being able to return to the school in any event, you did have the conference and the result was the same.
3. Given this is a private school they do have a wide discretion and can determine that they just do not wish to continue to have your son at the school they could do so for all manner of reasons and do not need to prove anything, the only exception of course is they cannot discriminate based on a protected characteristic such as race or religion but if it was down to that it would be for you to show it was that not the other way around.
In terms of the legal action you suggested above, well 1 may work but as I say it is not likely to help except potentially you get some nominal damages for breach of contract. 2 will not work for the reason I set out at 3 above and 3, libel and slander is an interesting one. If you wanted to bring a defamation action, you would need to establish that a statement has been made about you which would lower people's opinion of you in the estimation of right thinking members of society generally. Broadly, the test is whether a statement would cause one to think less of you. The other side can defend a claim under the grounds of justification, privilege or fair comment. In relation to the defences, Justification is a complete defence to the action of defamation (as long as the defendant can prove that the statement is substantially true). The defendant does not need to show that there is public interest in the publication or whether they acted maliciously. Privilege, does not apply here because this applies to circumstances such as parliamentary proceedings or court hearings. Finally, fair comment, is a defence if the defendant can show that the statement is an expression of opinion on a matter of public interest (and not a statement of fact. A matter of public interest is viewed by the courts as matters which will affect people at large to the extent that they may be legitimately interested in what is going on (or indeed what might be happening to them).The comment does however have to be based on true facts which are stated in the publication or are referred to. The defendant must prove that the underlying facts are true. The defence will not stand if it can be shown that the comment was made maliciously. In terms of the chances of being successful, as an area of law defamation actions tend to be difficult to win because of the range of defences available and because courts are reluctant to impinge and curb freedom of expression especially where the comment that is subject to the action could be seen as in the public interest. In relation to costs, it is not possible to say how much this might be with any great specifics because it would depend on the lawyers you would hire, the area of the country and the complexity of the case but such actions tend to be expensive and cost many thousands of pounds. Furthermore, even if you are successful in your action you are not guaranteed to recover your costs.
I trust this assists you in understanding your position however, should you have any supplementary inquiries, do not hesitate to ask and I will look to clarify or expand on my previous response.