Set O online form (Immigration problem in a country other than UK)

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I am on Tier 2 General visa and will be eligible to apply for ILR end of November 2018 (5 years completed). I was planning to submit the Set O form at a Premium Service Centre, but now the process seems to have changed and I hear that only online Set O applications will be accepted. All this is good, but I noticed that the online Set O form asks for a lot more questions than the paper one. There is one question that I am particularly concerned about, which is:

Problems with immigration to countries other than the UK

It asks about whether I was ever denied visas or refused entry at the border by any countries other than UK. Unfortunately earlier this year I had an incident, when I was going to New Zealand on a holiday. I had a valid tourist visa, but they put me through excessive screening at the customs (probably triggered by profiling based on my background), took my phone and confiscated it for investigation. They denied me entry and sent me back on the next plane to UK. They told me that the initial review revealed my phone contained inappropriate content. I was denied admission to NZ and sent back to UK.

I was not charged or convicted or anything and never had a problem relating to immigration in UK or any other country (and I have traveled extensively). I am looking for some guidance on the following questions:

1 - Is it still possible to submit ILR application using paper Set O form (if yes, until when?)
2 - If the only way application would be accepted is the online Set O form, what level of detail should be mentioned referring to this incident?
3 - How would this impact my chances of getting an ILR (considering I don't have any conviction or official charge either in the UK or any other country, just denied entry to one country)?

Would really appreciate some help as this new question on online Set O form has really got me worried. If anyone has any examples of similar cases, please share the details.