How do different techniques impact sourdough bread?
Lots of questions here.  Let me try to address them:


To knead or not to knead? I've heard people claim that kneading impacts flavour, then others claim it's the only way to get the highest rise.


It's true that kneading a lot can introduce a lot of oxygen into the dough, and that can have a small negative impact on flavor, which will mostly be noticeable in lean doughs (those with only flour, water, and salt, without enriching ingredients or flavorful additives).  This effect is relatively minor in the grand scheme of things, though.  It's more of a concern with intense mixing by machine rather than relatively slower and gentler kneading by hand.

The alternative to kneading is doing periodic stretch-and-fold cycles during the first proof.  In that case, you need to measure the length of your proof by time (and temperature), rather than when the dough "doubles."  But you need to do something to make gluten connections to maximize loaf height.  (So-called "no-knead" breads generally work by using very long fermentation, which will also increase gluten connections.  But if you're only fermenting for a few hours, you'll need to knead and/or do stretch-and-folds.)


Similarly, what impact does punching down the bread after the first prove have?


For most recipes, there's no reason to deliberately de-gas the dough.  The goal in shaping is fourfold: (1) stretching and folding the dough to make more gluten connections and increase structure (as mentioned above) which will increase loaf height, (2) stretching the outer "skin" of the dough to increase surface tension and support loaf height rather than spreading, (3) redistribute the yeast within the dough to provide them with new food sources, (4) in the process of moving the yeast around, move them away from high concentrations of their own waste gases (which tend to slow growth).

Only the last point is a rationale for actual de-gassing, and it's a relatively minor concern.  The main emphasis in shaping should usually be on the first two, and some de-gassing will naturally happen in that process.  Tight shaping to maximize loaf height will already result in de-gassing, but there's no reason to deliberately "punch down" the dough more than necessary in most breads.

The main reason to deliberately "punch down" the dough is to get rid of large bubbles that would create irregular "holes" in the final loaf.  If you're making a sandwich loaf or something where you want to avoid big holes in the final bread, there may be a reason to deliberately "punch down."  But in more rustic breads, baguettes, etc. which often tend to have more irregular holes, this isn't a concern.


I currently do a short autolysis, long first prove, short second prove - how will it impact my end product if I change these up?


What would you "change up"?  This is fairly typical.  Longer autolysis has diminishing returns, but it can be done.  You want the first proof to be longer to develop flavor and allow yeast growth.  (Longer first proof usually means more flavor.)  And the second proof is mainly to expand the shaped loaf to develop gases that will lift the dough during baking.  There's no reason to extend the second proof longer, and doing so would likely result in overproofing and collapse in the oven.


Some places have suggested that the long rise should result in the dough tripling in size. When I tried that, the finished loaf was more flat than normal: over-proved?


Sort of.  Particularly with sourdough, the yeast may not have sufficient strength to do too many long proofs.  Proofing too long with sourdough can also lead to more build-up of acid, which will eventually break down the gluten structure more (and is more likely to lead to a smaller rise or collapse in the final loaf).


If I went to 60% hydration, or 80%, what impact would it have on the finished loaf, and what would I need to adapt in the recipe?


It's hard to predict without knowing your exact recipe, flour type, etc.  Too low hydration will prevent elasticity in the dough and thereby result in a smaller rise.  (Think bagel-like interior texture.)  Too high hydration makes the dough harder to work with, though it also tends to help with a more irregular hole structure (which some find desirable) and a less "stiff" interior.  These are just general tendencies: changing hydration has lots of effects, and the specific recipe/technique will highlight or undermine some of those effects.  


When using my banneton, should I place the bread onto the linen, or the wicker directly?


You can do either.  With a medium hydration dough, it mostly depends on whether you want to wicker patterns to be seen strongly in the final dough to make a "pattern" on the top.  With wetter doughs, I find it harder to put it on cloth without excessive amounts of flour, and the wicker can sometimes stop sticking by having less dough contact (and also allowing more moisture to escape from the dough surface).


How would adding sugar impact my loaf?


Sweetness, obviously.  Faster browning.  Can potentially soften the crumb a bit.


Are the any other techniques for adapting sourdough loaves?


Lots.


My reason for asking, is that I want to start experimenting with shaping (hence different hydrations), and with different textures (i.e. soft vs chewy internal loaf).


More vigorous shaping is generally helpful in increasing dough height, as mentioned above.  Gentle shaping is most useful with high-hydration doughs where you want an irregular hole structure in the final loaf.

Regarding texture: the easiest thing to do to create a softer interior (like traditional "sandwich bread") is to enrich the dough by adding butter/oil, eggs, milk instead of water, sugar, etc.  Higher hydration can also help a bit, as well as using a lower gluten flour (though this can decrease loaf height).  Do the opposite if you want something more chewy.