Red,Blue,Purple,Yellow,and white
If you are talking about pikmin 1 then there is the infected pikmin.
Up to 100 Pikmin can be outside at a time. This includes wild Pikmin of colors you haven't discovered yet.
The original Pikmin had no way of switching between colors of Pikmin on the fly. To switch colors, you need to disband your Pikmin with Y or C for Wii version and call the appropriate color to you. You can alternatively hold the throw button and press the whistle button.
You have to leave Pikmin idle by a Puffstool and call them at the exact moment they are hit by the Puffstool's spores. This requires perfect timing. Be careful, as Mushroom Pikmin will attack any other kinds of Pikmin.
More purple and white Pikmin can always be gotten by throwing Pikmin into Ivory and Violet Candypop Buds, respectively. For the colors of Pikmin that have Onions, a single seed of that color will pop out at the beginning of the next day after what is called a "Pikmin Extinction".
No there is not a Pikmin that will give you more or additional Pikmin.
All five original pikmin have been confirmed by Mr. Miyamoto. In addition, as you have probably already seen,, are the rock pikmin. These, despite what people have been saying, are not like purple pikmin at all. Really the only similarity is they give a little umph when landing on an enemy, and even then, they attack by repeatedly throwing themselves at the enemy instead of latching on, and don't have the possibility of making the enemy dizzy, like the purple. A flying pink pikmin with blue eyes can be seen in the trailer for a brief moment at the beginning and end. It doesn't really give you a clear view, though. When confronted about it, Nintendo said they couldn't confirm nor deny the pink pikmin. They did, however, confirm that new unannounced pikmin would be seen later in the game.
No. White Pikmin made their first appearance in Pikmin 2.
Mushroom Pikmin are Pikmin that have been transformed by the spores of a creature called a Puffstool. Affected Pikmin turn purple and try to attack Olimar and normal Pikmin. This effect wears off after a while.
In Pikmin for the wii you need have a group of pikmin by you then press 1 and the pikmin will carry you back to their onion.
Although it's an unconfirmed pikmin, it will most likely to be nature
Yes. The graphics in Pikmin 2 improved noticeably over those in the original Pikmin.