It is not a question of section 5 coming before section 1. That isn't how it works. It is not for a website operator to judge whether or not section 1 has been contravened. That is up to the courts. But when the website operator receives a complaint they have limited time to act.
If a school (or anyone else) notifies Mumsnet that a post is defamatory Mumsnet has 48 hours to deal with the complaint. Within that time they must either enable the complainant to resolve their dispute with the poster or remove the post. The clock starts ticking as soon as Mumsnet receive a complaint with the prescribed information and does not stop for any reason. If at the end of 48 hours Mumsnet has failed to take the required action they lose their section 5 defence and can be sued along with the poster. The courts will then decide whether or not section 1 has been breached.
Libel damages can be very high. If Mumsnet receives a complaint and ignore it their insurers may be able to refuse cover. It is therefore sensible for Mumsnet to treat any complaint that a post is defamatory seriously and take appropriate action unless they are very confident that the post is not libellous.
By removing your post Mumsnet is not judging whether or not you have defamed the school. They are simply protecting their own position. It means the school can sue you (provided they can identify you) but any action they take against Mumsnet will fail.
The 2013 Act only came into force on 1 January 2014 - no case would make it to full trial in that time. If there have been relevant proceedings for emergency injunctions this year, I'm not aware of them.
LadyMary MNHQ have been hit with the Section 5 : they have been great but I'm trying to find out both theirs and my position. Many of the other people who got the same email have had their posts deleted I have chosen not to as I believe in free speech but have to balance rightness and sanity
hence my search for current legal thought about what will get through section 1 and whether 5 comes before 1
The fundamentals of UK law is that they can not change the past. It would be pretty silly to make a law in 2014 that legislated prior to this - you could find that you were arrested in 2035 for spitting on the floor in 2014 because there's a new law in 2034 or something so it's just impractical. See what I mean? If it's a previous problem then it will come under the previous laws and regs, not the new ones. HTH.
If a website operator refuses a section 5 request they have lost their defence against. It is therefore sensible for them to take a cautious approach and either enable the complainant to resolve the issue with the poster or remove posts that are reported as libellous unless they clearly are not.
I am not sure what you mean by leeway under section 3 and I don't understand how you think the litigant's actions could "turn section 3 into section 2". You need to consult a lawyer specialising in libel and slander if you need authoritative answers.