I don't see any rubber covering those 200V 470uF caps, only the usual plastic heatshrink on the sides and plastic disks on top for electrical insulation. It's common for high voltage caps to be covered on top, and it's also common for those plastic disks to bulge from years of exposure to heat originated inside the cap, even if the cap is still perfectly good. You may want to remove the most bulging plastic disk to see if the metal can is leaking or bulging on top. Electrolytic caps can't be tested with just a multimeter's ohms function (cap starts out as a short and gradually shows higher resistance as it charges) because many test normally that way and even show correct capacitance, but their ESR will be 10 times normal. If you replace those 200V 470uF caps, a rating of 85C is perfectly adequate because those caps work at low frequency, 120 Hz, and there won't be much benefit to installing 105C caps. But 105C can help significantly for caps that work at high frequencies or that switch square waves, such as in the secondary side of the main power supply or the flyback supply (horizontal output section), although 105C alone doesn't indicate suitability for such circuits. Detailed information can be found in the Digikey and Mouser print or PDF catalogs (harder to find it in their regular online catalogs) or the capacitor catalogs put out by manufacturers like Panasonic, Nippon Chemcon/United Chemicon, Rubycon, Nichicon, and Sanyo. Your TV appears to have Chemicons and Sanyos, two very good brands of caps. While high frequency and switching caps should be of low ESR, generally it's bad to choose caps of the lowest ESR for TVs because they can cause unwanted oscillations.
In your Photobucket album, I see a cracked solder joint in photo #8, between the 2 holes at the bottom, and in photo #11, in that circle of solder joints (is that the board that plugs into the back of the CRT?). Photo #9 has at least 2 solder joints that could have been made with dirty wire leads (ring of flux around each), but that may just be shadows, and the same may be true in the middle, near the bottom, of photo #10. Photo #14 shows some power rectifiers and thermistors. The pink thermistor seems to be touching the grey boxy capacitor, and I'd probably bend it away so it doesn't do that. The white plastic boxy object in front of that thermistor may be another thermistor, for the degaussing wrapped around the front of the CRT, and that thermistor can remain so hot for long periods that it almost melts its own solder connections. Or it could be a relay, also for the degaussing coil. It's generally good to resolder the joints of all devices that run hot, including large resistors that stand well above the circuit board for cooling (blue devices in photos 1, 6, 7, 12, 13), large diodes, transistors, and chips, and generally anything in an area of the board that's darkened from heat. Also resolder joints in mechanically stressed locations, such as connectors, heavy devices (transformer, flyback).
Data sheets for horizontal output transistors should indicate whether the damper diode is built in or not. The NTEinc.com substitution manual should also indicate such informaiton. With Japanese transistor numbers, prefix 2s to the part numbers printed on them, that is, a transistor labelled C3039 has a full part number of 2SC3039. When installing components to heatsinks, use proper insulation, usually a silicone rubber, Kapton, or mica insulator and a nylon flange washer for any screws, and silicone heatsink grease. If you have to buy an insulator, get a high voltage version since they're also made in low voltage versions that can quickly cause a short. Use silicone heatsink grease made for electronics repair, not anything marketed specifically for computer CPU heatsinks since the latter often conduct electricity, especially when they're made with silver powder (Arctic Silver). If there are no electronic supplies near you, try auto parts supplies and ask for dielectric grease for ignition modules.
In addition to the main power supply and horizontal output section, you may want to check the vertical oscillator/sweep section since a few caps there are prone to wear, even values as small as 1uF. A single chip likely handles all the vertical functions and possibly even much of the horizontal functions, and the chip's data sheet and application notes may be of help and include an example schematic. Some libraries carry Sams Photofacts (Sams, not Sam's), either in paper form or online, and Elektrotanya has some free factory manuals.