Emergence Cave, Subterranean Complex, Frontier Cavern, Hole of Beasts, Bulblax Kingdom, Snagret Hole, Citadel of Spiders, Glutton's Kitchen, Shower Room, Submerged Castle, and Cavern of Chaos.
No, they did not exist at that time. Only red, blue, and yellow Pikmin are available in the first Pikmin game. There are only white and purple Pikmin in Pikmin 2. They have no Onions, and can only be found by tossing any Pikmin into purple or white Candypop Buds. These flowers can only be found in underground caverns, which were not present in the original Pikmin. The flowers disappear after a certain amount of uses, and thus only certain amounts of purple and white Pikmin can be attained at one time.
The easiest way to get white and purple Pikmin is to go into easy caves, find the Candypop Buds and transform Pikmin, then get out. Keep in mind that Candypop Buds do not reappear in the same day after leaving a cavern. Emergence Cave in the Valley of Repose is best for purple Pikmin, and the White Flower Garden in the Awakening Wood is best for whites. Relatively easy caverns that can be used to get white and purple Pikmin are the Snagret Hole in the Valley of Repose and the Citadel of Spiders in the Perplexing Pool.
Just keep reproducing them. Bring enemies or pellets back to the red, yellow, or blue Onion and either red, blue, or yellow Pikmin will sprout into the ground. Have Olimar or Louie press "A" on them to pluck them out. However, if you are looking for purple and white Pikmin, you need to go into caves. Some caves contain flowers on the ground which are called Candypop Buds. The Ivory Candypop Buds will produce white Pikmin sprouts when you throw any pikmin in them, and the Violet Candypop Buds will produce purple Pikmin. These can only be used a few times. If you are grinding, I recommend the Subterranean Complex.
By far, the strongest color of Pikmin is purple. Purple Pikmin count as ten Pikmin when carrying objects and are so heavy that they stun enemies when thrown.
Red Pikmin are arguably the simplest Pikmin, in both form and function. They have high attack power and can withstand fire, whereas the other types of Pikmin look stranger and have a wider variety of uses. Also, you do not come into fire hazards early in either game, which means the more common electric and water hazards block a larger area of the world. Lastly, white and purple Pikmin could not be the first Pikmin you get in Pikmin 2 because they can only be created in caverns you need Pikmin to enter in the first place.
Ivory Candypop Buds (the white flowers that give you white Pikmin) can be found in underground areas. Going into the same cave that had the Candypop Buds will cause the flowers to reappear. The White Flower Garden has several Ivory Candypop Buds, but they only appear if you have a total of 20 or fewer white Pikmin. Violet Candypop Buds (the purple flowers that give you purple Pikmin) are also found in underground areas and can be replenished by waiting. The best areas for finding them are the Subterranean Complex and the Hole of Beasts. The Crimson, Golden, Lapis Lazuli, and Queen Candypop Buds can be found and replenished similarly.
Red,Blue,Purple,Yellow,and white
The blue pikmin are in the Awakening Woods but first you have to go to the Perplexing Pool, beat the Fiery Bulblax and get the yellow pikmin.Now return to the the Awakening Woods and at that area where you had a black gate, and fought your first Cloaking Burrownet, and Creeping Crissanthamum throw your yellows away from the Cloaking Burronet on that ledge get Olimar or Louie/Mr.President, get your yellows beat the Burrownet and tear down that electric gate(reccomended that you have 30 yellows for this).Now leave your yellows their after that gate is torn down and go to the other side and their you have it tied for best in Pikmin and tied for third best in this game blue pikmin.
Unknown, maybe working with seven different types of Pikmin at the same time would make the main story too complex.
Creeping Chrysanthemums are a type of enemy. They look like ordinary flowers (albeit with eyes) until you approach them, in which they turn into a vicious enemy that can devour your Pikmin. To prevent this, either trick the plant into snapping itself or throw purple Pikmin on it to stun it. You can see a picture and find out more information regarding the Creeping Chrysanthemum in the related link below.
You can't. Your only choice is to avoid the Waterwraith and carefully collect treasure. On the final sublevel, you can get purple Pikmin, which allow you to defeat the Waterwraith.
Mr. Miyamoto has confirmed both. Nothing else has been said other than they will be in the game, though.