What’s the difference between yellow and orange fire

I doubt anyone can actually give you a completely accurate answer without doing something along the lines of disassembling the game or being Edward McMillan, but after a rather successful run I think I can shed some light on this.

Chances of getting rare bosses: Boss enemies can be encountered not only on actual boss rooms, but also in seemingly ordinary room (this is especially common in The Womb). To me, it seemed that the frequency of special bosses is on par with the frequency of other special enemies, which in turn depends on the level you are on, as harder levels contain more rare enemies. When travelling in the womb, I'd have to say that 1 in four bosses I came across were rare, and less so on the easier level.

Do rare bosses drop anything special: Assuming an empirical answer can be provided for this, then after dispatching of at least 10 rare bosses, 3 of which in an actual boss room, I would have to say that the answer to this is no.

There is also the matter of Alt-Bosses, which are not a rare boss strictly speaking (they are more of a re-skin than a pallet change). These do drop specific special items as can be seen here and here.

Are there other differences to rare bosses: There are at least three that I am aware of, though I suspect there are many, many more. Here are a few examples from my latest run:

This green colored Chub was actually slower than the regular Chub, and spawned boils instead of maggots. Be aware that the color doesn't necessarily indicate the rare boss's properties, as this page lists the version I described as black, and the version you described as green.

I encountered this darker version of Monstro, which was slightly bigger than a regular Monstro. I can't say I noticed any additional differences. I also had a chance to encounter Monstros that are smaller than usual.

This green/lime version of Larry Jr. actually fires projectiles at random, much like the Gusher enemy (and also makes a green mess of the floor).

Like I said, I suspect there are even more variations (some of which are chronicled in this wiki), but these are the ones I came across.

There is no foolproof way to find the secret room (except with some of the items you can pick up, like x-ray glasses), but 99 times out of 100 you can find it with one method and a little luck.

Most secret rooms are contained in between at least 3 other rooms. All you have to do is look on your minimap for 5 rooms that are all joined in a square "U" shape (3 on the bottom, and 2 for the sides). Bombing in the middle of the wall that faces towards the gap in the U from any of the 3 rooms that will share walls with the room will lead you in.

You can then bomb your way out into another room if you so choose. This can be useful in getting into the treasure room with no keys if the secret room borders the treasure room.

Some maps have more than 1 "U" shape in them, in this case you're just going to have to guess and hope to get it on your first go.

Some maps won't have even 1 U shape, in this case, the room will probably be in bordered by 2 other rooms, so look for a set of rooms in a square "r" shape and hope that the one you picked is the right one.

The super secret room (Wrath of the Lamb DLC only) is found in a different way. The super secret room will NEVER border more than one room (except very rarely the regular secret room).

To find the super secret room, look for any walls where if there was a room on the other side, it would have no other entrances, similar to the treasure rooms and shops.

Unlike the secret room, the map (or the tarot card "The World", or any similar items) won't show the super secret room. X-ray glasses and the Spelunker hat will still work however.