Keep it simple please.

Install a sub with it's own amp.
You can just replace the speakers but for limited gain as you really need to also install an amp to drive them. No aftermarket speakers will sound much better being driven off the 2 x 20w internal HU amp (non Bose).
If you have the Bose sytem then the speakers are 2 ohm impedance so again replacing with 4 ohm AM speakers will not sound much better (possibly worse). The biggest bang for your buck is to install a proper sub, giving you a huge improvement in bass but also reducing the bass to the cabin speakers so you can drive them harder with less distortion.

No & no.
The standard enclosure is plastic, so only useful for keeping your biscuits in TBH.
The standard sub amp is puny and is also driving the rear speakers so can't be used.
If it's just to placate passengers complaining in the rear, rather than an increase in quality your after, then replacing the original door speakers will help as the standard units are hopeless, but make sure you go for proper 2 way components with good tweeters.
Rear shelf speakers are a complete waste of time. Don't worry about cabling as there isn't enough power anywhere in the system capable of frying anything.
So for a quick fix I'd replace all the door speakers which will improve the clarity.
for a proper job you'd need to add a 5 channel amp for cabin speakers and sub, and lose some boot space with a proper sub/enclosure. This is quite a big job with a lot of cabling but will give you decent sound.
As a go between you could swap the HU, and run all the cabin speakers off the infinately better internal amp (something like 4 x 60w). This would require minimum cabling in order to run the rear speaker cable back up to the HU, but you would then need a couple of fitting adapters to link up to the Audi wiring for the sub, an aerial amp and a fascia adapter.
Sorry there's no quick fix.