I used to be an arborist and am still involved in trees (just in a different capacity).

@Slatlun has got it all right, though I would just add that the recommendation used to be 1/3rd (33%) of canopy but keep in mind that less is better so often a MAXIMUM pruning amount is 25%-33%. But, pollard and coppice exist which is a 100% pruning technique so there are exceptions to every rule.

That said, no tree would theoretically "like" to be pruned so if you can get away with <5% then that's the best option. Depends on what you are going for. The "just a bit more" feeling is constant when pruning, particularly when using a chainsaw, so that's something that needs to be mentally fought. Small and steady, observe, make longterm decisions on what's going to happen years down the track.

Gorgritch has made the correct observation that often pruning is associated with tree health, including tree health in relation to growing seasons. And to add to that, if you are pruning deciduous trees, you always prune the theoretical day before bud burst (which translates to some period later in Winter by a couple of weeks but every year is different).

There is even a correct way to use the secateurs that most don't know about. The sharp part of the blade (not the blunt bypass or anvil part), has to be on the inside of the cut, leaving a smoother non-bruised edge on the plant part you are keeping. This means when pruning a tree, the secateurs will be constantly being turned around in your hands before you make the next cut (if required). Someone learning pruning might not notice an arborist flipping the seccies before they make the next cut because usually the arborist is operating a few cuts ahead in their mind.

To answer your question regarding trunk strength, there are a lot of factors. Was the tree tied up after planting? Was it over-fertilised (even the supplied fertiliser in original pot can have an effect) or is it a species growing in a slightly different soil type or did it have excessive rain? Genetically, did you get unlucky or is this how it wants to grow (can you compare to other trees of the same species in a similar location)? So many questions to ask. Removing lower branches often decreases trunk taper making it more likely to bend and blow around so I would consider what you heard there maybe unlikely to help but you never know.

The easiest way is to perform a height reduction on the tree. This will set the tree's height back, give it more time to increase trunk diameter while reducing the weight and sail effect from wind. The trunk may stiffen up while the tree replaces that height again. Reductions are a common though more advanced pruning technique. It's hard one to explain but you are selecting for a new leader that you can imagine will become the head of the tree years later. But, the branch you cut back to has to be the right size in relation to the trunk that is cut... blah blah blah. Have a look at a few guides for reductions online.

I'm not from Austrailia, but the general rule for pruning is that up to 30% of the crown is ok, so I wouldn't worry at all about 10%.

This might already be your plan, but the best branches to prune are the ones with the most leverage. Those are the tallest and longest ones. The least effective will be the shortest, lowest, and closest to the trunk.

Unnecessary info: Trees need leaves to make food, but leaves use water and other soil nutrients. Trees need roots to gather water and other soil nutrients, but roots don't make food. The balance in pruning is between these two things. Cutting off branches in the hot and dry will probably actually help the plant survive because you are reducing water demand during a time when food is plentiful. The trick is to not overdo it and starve the roots. That's where that 30% idea comes from. Almost every plant will tolerate that amout of cutback without taking root damage.

I know nothing about pruning, and am really interested to follow this thread as well.

In saying that, my general rule has been general pruning only during autumn or spring. If theres a dead branch then anytime, the sooner it comes off the better. Always clean the cutting implement before and after use, to remove any nasties. I'll usually give the plant a good drink after pruning as well.

I have no idea whether i'm doing the right things here or not though.