For capacitors, look for brands like Nichicon, Panasonic (also known as Matsushita), Rubycon, Nippon Chemi-Con (also known as United Chemi-Con, formerly Marcon), and Sanyo (nowadays known as Suncon). 

So far had not had to replace any resistors, except for that 0 Ohm link. As for resistors, depends on the original resistor being replaced and should follow the wattage of the original resistor (in other words, the size of the resistor determines the wattage). The diode is pretty much run-of-the-mill 1N4004, which is a very common diode.

That one very much depends on whether you're going to replace them, and/or depends on the fault/problem itself. The "funky" look is mostly leftover excess flux and not degraded glue. If any of those MOSFETs had blown/failed then you will need to replace them.

Try online stores such as RS Components, Farnell/Newark/element14, Mouser and Digikey. They are guranteed to sell original capacitors (and not those Pasar Road counterfeits).

Just change all those 85C capacitors to ones rated for higher temperatures, such as 105C ones (as shown in my guide here). Preferable to use those with high ripple current handling and/or low ESR type, as this speaker uses switching mode power supply...

That's not a "ceramic resistor", but a ceramic disc capacitor. Just replace with another one, of the same capacitance. Usually should be 100nF or 0.1uF, 50V or higher.

digikey shipping exp if i am not mistaken

This one is incorrect as its rather wider than the original. The diameter should be 22mm otherwise the capacitors will not fit together. Should be this 22mm diameter version (if using Mouser): Mouser > Passive Components > Capacitors > Aluminum Electrolytic Capacitors > Aluminum Electrolytic Capacitors - Snap In > Panasonic EET-ED2D471BA...

Incorrect one again, as the lead pitch is 3.5mm. Should get the version with 5mm lead pitch. Digikey > Capacitors > Aluminum Capacitors > UHE1V221MPD6...

Look for Nichicon HE series, like this one: Digikey > Capacitors > Aluminum Capacitors > UHE1E470MDD.

If you are talking about the cracked ceramic disc capcitor replacement then it would work. Like I've mentioned earlier just any 100nF or 0.1uF ceramic capacitor of 50V or higher rating can be used (even those cheaper but awful Y5V ceramics), since this capacitor is non-critical (functions as low impedance side for those original general purpose 85C capacitors). However, for the capacitor that is very close to the heatsink (which is actually part of the switched mode power supply feedback section) then stick to the capacitor I've specified (for stability reasons use either X8R, X7R or NP0/C0G ceramics).

Sounds much like the power supply section blew, possibly some weak, failed and/or faulty components. Usually should be fixable/repairable...

Yups, can use the same capacitor (that more expensive X8R high temperature ceramic) for both.

Either ones should be fine, just different packaging from the details on the website. Another option would be Nichicon PW series (slightly higher specifications than Nichicon PS series).

Their specifications are much lower than the Nichicon CS series. Here are some similar capacitors (with way better specifications than the ones you've chosen): Mouser > Passive Components > Capacitors > Aluminum Electrolytic Capacitors > Aluminum Electrolytic Capacitors - Leaded > Panasonic EEU-ED2W680 (used in the 2nd repair) and Mouser > Passive Components > Capacitors > Aluminum Electrolytic Capacitors > Aluminum Electrolytic Capacitors - Leaded > Panasonic EEU-EE2W680 (used in the 3rd repair which was not shown here). Both of them are also high ripple current handling plus long life...

That's typical as the chemical from the degraded glue has "eaten" into the solder resist layer (that green thingy). Usually its still workable, as long as you did not break any fine traces. Make sure those traces are still connected to each other, and check for possible shorts with surrounding copper areas (e.g. bits of copper layers pulled up and mangled). There are large areas of copper that is mostly either (hot) GND or +350VDC (or +154VDC for U.S version). Removing degraded glue from that resistor (encased in heat shrink tubing) should have been a piece of cake (and I did not have to remove that resistor) but not sure how you've gotten that "ugly" (lots of scrape marks can be seen). What tool did you use?

Must have patience, padawan. As mentioned some time ago (here: Post #11), degraded glue removal can be very tedious and have to proceed slowly (and carefully/meticulously) to avoid damaging/breaking PCB traces. When using a sharp knife, try avoid directly touching the PCB (otherwise there will be deep scrape and scratch marks, and possibly damaging/breaking fine PCB traces)...