Since you’re on a points website, I’ll assume that you’re hoping to use points for the tickets.
Finding four seats on the same flights may be a stretch. You might need to split the group and travel separately to make it all work - either through different cities or on different dates or times. But if you’re flexible and patient, you can get lucky. And as mentioned, February is low season.
Buying Lifemiles can work out cheaper than paying for premium cabin seats, particularly during a promotion, and if my sums are correct this could mean paying around $3600 per person for a return business class ticket from Australia to Europe. But I would argue that it’s more hassle than the saving is worth. Lifemiles can be complicated and frustrating, particularly for someone who doesn’t have a lot of experience in points redemptions, and I’m guessing you fit into that category, which is why you’re posting here?
Online options to buy frequent flyer points to your advantage are limited… The best buying deals are generally bonus promotions (Lifemiles has offered various bonus deals that see miles as cheap as 1.35 US cents per mile), or big sign-up bonuses for new credit cards.
I’m not familiar with Adelaide Airport, but I think Singapore Airlines is your only one-stop option with Lifemiles. Singapore Airlines often limits reward seat availability to those not booking through their own KrisFlyer program. If you can’t find anything with Singapore Airlines you could try getting to Melbourne, Sydney, Perth or Brisbane first, and then flying Thai Airways (or other Star Alliance carrier) from there to Frankfurt. With Qantas points, you could try flying via Doha on Qatar Airways. Both Thai and Qatar offer other destinations in Europe to consider if you are struggling to find Frankfurt flights that suit.
The cheapest route to get there… It’s all much the same when it comes to points, just watch out for flights via London Heathrow which imposes notoriously high taxes. If you want to buy tickets with money rather than miles, I can see one-stop flights for $1200 with Singapore Airlines or Qatar in economy, I would say these are both good choices. Cheap paid business class flights often have two stops to go from Adelaide to Frankfurt, with one in Asia and another in the Middle East or Europe, and they start at $5000.