a) It depends on the way the tank is made. Tanks fall into one of two types (broadly speaking, there may be exceptions I'm unaware of

). Some have a flat bottom where the entire base of the tank is in contact with the stand. This type needs a base mat or a layer of polystyrene. Any slight imperfection in the stand or even grain of sand between the glass and stand can cause the tank to crack. The other type is called a floating base. The sides of the tank project down beyond the base and the tank stands on a rim of side glass. The projecting part is often covered with a trim to make it look nicer. This type must not be used with a base mat. Some manuals even say that use of a base mat invalidates the warranty. There is a variant of floating base tank - my 50 litre is flat bottomed but it sits in a plastic frame which converts it into a floating base.
I've just looked at the setting up article and it says (my italics)
Finally, if the aquarium has an unsupported base, make sure you place a layer of polystyrene or foam between the aquarium and its stand or cabinet. Without a layer of foam or polystyrene, the aquarium base is prone to cracking when placed under the full weight of its water.
but it doesn't explain exactly what an unsupported base means.
b) That is the most recently developed way of cycling. The chap who devised this method did so in order to stop the nitrite level going off the top of the scale. Both ammonia and nitrite at too high a level can stall the cycle or even grow the wrong species of bacteria. The traditional method caused high nitrite. It is at levels of over 15ppm that the problems occur, but most testers only go to 5ppm. So if the nitrite shows 5ppm, it could be 5, 6, 10, 20 etc and you wouldn't know which. And unless you have distilled water and a means of measuring very accurately you can't dilute the sample to find the actual level.
c) Yes you can plant at the start. The main downside is that you have to have the lights on for the plants. There will be ammonia in the water at the beginning, and lights + ammonia = algae.
Unless you plant very heavily with fast growing plants, they shouldn't make much impact on the ammonia level - plants can use ammonia as food and if you have a lot you think the ammonia is dropping because the bacteria are growing but it is really the plants using it. Be guided by the appearance then disppearance of nitrite. Plants don't use that.