I booked a DGLOB34 last year. As with everything BA, when it works it's great and when it doesn't it's a nightmare.

You need that fare for business class that includes QF codes on Air Tahiti Nui. I didn't do this, preferring QF codes on Fiji Airways (the BA codes weren't in place at this time). I don't believe *ONE4 fares allow non-OneWorld metal, *GLOB34 fares will.

The OneWorld forum on here is a good resource, take time to read it all. Ex-UK will be about £6.2k, maybe more. Oslo is £4.2k, it's very much worth going the night before and staying at Oslo, and still having £1500+ in your pocket. Fares are filed in USD, so there's no difference in € countries that I could find, and the saving from those wasn't sufficient to justify not going from the UK. Sweden and Denmark were north of £5k, Oslo was the clear winner.

Check the rules for overland segments, I haven't had to consider them, to know if this is a penalty you'll hit on your mileage or segment depending on your ticket. GCMapper is your friend for staying within mileage rules, but generally something like OSL-LHR-DOH-SIN-SYD-DRW//ADL-SYD-AKL-PPT-LAX-JFK-BOS-LHR-MAN-HEL-OSL is likely to be fine (check this, I haven't!!)

For booking, BA Newcastle are wonderful, expect a lot of HUCA. Sunday mornings at 8am were best. A couple of AA segments mean inevitable schedule changes thus free changes - really valuable for me during COVID when countries hadn't opened up yet. When such a change happened and I had 4 separate calls to South Africa and India, they made a massive mess that took Newcastle 20 minutes to just read the notes, cancel it all and rebook it 'neatly', so ensure you get them first. When you get a good person, ask if they can send you a direct email and that they'd be happy to communicate via email for any changes, it makes a big difference.

Finally, use the full mileage and allowance if you can! Plan that Euro trip on the side. Make an out-of-the-way detour, maybe from SIN on Malaysian. Check whether QF codes on Jetstar are allowed and you could do a little NZ exploring. These tickets make the world seem tiny, and they are addictive.