Saw all this and thought I'd weigh in from experience of building the kit and a few p/p clones. Im a lapsed engineer and just sling solder as a hobby. I did build a few 'clones' and stay in a holiday inn, so I hope this helps. This is specific to your questions vs a EE dissertation.
1. The 33uF and 20uF capacitors inline with the power supply are called "signal" or "smoothing" capacitors. These function to smooth the signal and voltage presented by the power transformer. The suggested bypass capacitors (anniversary modification) further filter and improve the signal. Upgrades here can create dramatic improvements
Ans) Filter/smoothing/reservoir pick a name. With a tube rectifier you have limits on the first cap. Increasing the value of these caps, say 47uf will reduce ripple, which manifests as a low freq. hum. You will hear ripple in you speakers with no signal. These caps take the AC rectified into DC spikes and "smooth" it out. Since power supply feeds B+, direct to your speaker, the better / smoother this signal is, the better....Within practical limits, and the design.
Upgrades here (eg bypass caps) reduce resistance in the PS caused by larger value caps and ostensibly improve speed and sound. Bigger caps used to have very high ESR, these smaller "bypass" caps reduce the overall ESR of the power supply and "speed it up". The power supply feeds B+ and signal directly. Subtle/modest changes at best IMO. Invest in your "coupling" caps vs these if you have a choice.
2. I am unsure of the naming and the function of the 3.3uF capacitors with the 10K resistors. Do these set the B+ voltage? I understand these have been dropped from the later iterations of the production amplifiers.
Ans: Voltage divider to feed preamp tube. They have been dropped AFAIK. I have had success removing them and using 2 56K carbon. If you have a good power supply this "works". I have made this change on my amps.
This sets voltage for preamp tube, it comes after B+ in the circuit. B+ is fed from Power supply (see above), before this filter.
3. The two 0.1uF capacitors between the input and output stage are "coupling" capacitors and passes audio signal without a steady DC voltage and associated interference. Upgrades here can improve sound and performance, but not necessarily to the extent of the power supply upgrades
Ans) This is the sound of your amp. Upgrades here are generally accepted to improve quality. See Paper in Oil/Beeswax whatever Mojo. Good caps here matter.
4. The 0.1 uF capacitors are the "Hazen Modification" that is specific to pentode and called a "suppressor" capacitor and manage electron flow in the tube. There is a lengthy discussion on this by Mr. Deckert.
Yep.
5. Lastly, the 1000uF capacitor is a "cathode bypass" capacitor in may influence gain, frequency response and hum. Any idea which of these are functions are the purpose of this capacitor along with the resistor.
Ans) Set bias level (current) for output tube. The cap works as you describe above. I suspect all 3, mostly gain and frequency response. You deal with hum upstream

. Ive heard of people bypassing this cap with a smaller one too. YMMV
Best I got off the top of my head. Hope this helps.