You can only use one transformation per battle. The pl increase only last until the end of the battle as well as the damage increase. The part about who can perform the ability is just a little information from the manga/anime/and movies so you know who was able to do what.
Saiy-jins:
Super Saiya-jin-Probably the most popular form of battle in Dragon Ball Z from the defeat of Freeza to the end. This is something only Saiya-jin or human/Saiya-jin hybrids can accomplish (example: Gohan, Goten and Trunks). When a Saiya-jin is in the Super Saiya-jin state, their hair turns a blond color, their eyes turn turquoise and they are usually surrounded by a yellow ki. The state of Super Saiya-jin is accomplished by attaining several requirements. The Saiya-jin must have a quiet, pure and calm heart. The Saiya-jin must also have a certain amount of power. Vegita knew Gokou would be able to attain Super Saiya-jin when he demonstrated his skills against the Ginyu Tokusentai at a power level of 90,000. The final requirement is extreme rage and lust for battle. This is why it was so difficult for Gokou to attain SSJ, because he's not normally an angry person. Once in the SSJ state, the Saiya-jin's heart is filled with anger. Because of this, Gokou cannot form a Genki Dama when he's in the SSJ state since he needs to have a pure heart to do so. An interesting fact is that the SSJ we normally see, (the blond hair etc.), is actually a weird transformation. The true Legendary Super Saiya-jin who existed 1,000 years before Dragon Ball Z did not change in that fashion. He became a golden Oozaru. The reason Gokou and the rest change differently is because their tales are removed.
Who can perform it:Son Gokou, Son Gohan, Son Goten, Vegita, Trunks *Future and present*, Gotenks and Vegitto *In the movies only, Brolly was the Legendary SSJ*
Pl must be 30,000. When you use this attack your pl increases by 10,000. You also get an extra 500 damage to your total attack damage.
Super Saiya-jin Dai 2 Dankai "Ultimate Super Saiya-jin Stage 2"-The Ultimate SSJ state is used briefly in DBZ right before the Cell Game. This state of SSJ increases the Saiya-jin's power, but not by much. The state itself looks pretty cool though because the Saiya-jin's body becomes totally pumped up.
Who can perform it:Son Gokou, Trunks and Vegita
Pl must be 45,000. When you use this your pl increases by 12,000. You also get an extra 1,500 damage to your total attack damage. When in this form you can only have 4 attacks per turn due to ur massive size.
Super Saiya-jin Dai 3 Dankain "Ultimate Super Saiya-jin Stage 3"-This stage looks REALLY cool, unfortunately it's only used in battle once. The Saiya-jin's body becomes HUGE and muscular. The picture of Trunks in this state in the manga is really cool because his entire body fills the picture. The Saiya-jin's power is increased by a huge amount during while in this state, however because of the muscular pump-up, the Saiya-jin is very slow moving and can leave openings for attacks if their opponent is skilled enough to spot them.
Who can perform it:Trunks and Son Gokou
Pl must be at 60,000. When you use this your pl increases by 15,000. You also get an extra 1,750 damage to your total attack damage. While in this form you can only have four attacks per turn due to your massive size.
Super Saiya-jin 2-Super Saiya-jin 2 AKA "The Super Saiya-jin beyond Super Saiya-jin", was first seen being used by Gohan in the Cell Saga. Although it's arguable as to when he first really reached this level. (Some say in the Room of Spirit and Time, some say during the Cell Game) It's clear that this is the most suitable form of SSJ to be used in battle with strong villains. The Saiya-jin's power is increased immensely and their speed does not suffer at all. And unlike Super Saiya-jin 3, it does not use up the character's energy as quickly.
Who can perform it:Son Gokou, Son Gohan, Vegita and Gotenks
Pl must be at 80,000. When you use this your pl increases by 25,000. You also get an extra 1,000 damage to your total attack damage.
Super Saiya-jin 3-The most powerful SSJ attained in DBZ. SSJ is probably my favorite level just because it looks so COOL! The Saiya-jin's hair turns blond and their eyes turn turquoise, but the major change is that the Saiya-jin's hair grows to an incredibly long length and their eyebrows disappear. SSJ3 Gokou may even have been the strongest character in DBZ. Gokou says that if he were to reach Full Power SSJ3 he could defeat Kid Buu. Unfortunately, he never reaches Full Power because being in the SSJ3 state uses up a LOT of energy and Gokou ran out of energy before he could reach Full Power.
Who can perform it:Son Gokou and Gotenks
Pl must be at 130,000. When you use this your pl increases by 60,000. You also get an extra 1,500 damage to your total attack damage.
Androids:
Imperfect Android: This is the state that Cell obtained when he absorbed 17. He transformed into a more human looking creature then in his normal form. He Grew taller and his tail became a ltiile shorter. His power also increase significantly.
Who can perform it: Cell
Pl must be at 25,000. When you use this your pl increases by 7,500. You also get an extra 350 damage to your total attack damage.
Perfect Android: This form was obtained by cell when he absorbed 18. He transformed into something that resembles a creature more then a human. His power greatly increased. He grew wings, had his tail retract into his back, and was a little shorter then his second form. He first used this form on Vegeta and completely destriyed him. It wa then Trunks who tried to take him on, but Trunks too found out that he was not strong enough. Son Gohan then punched android 18 out of Cell and he had to revert back to his imperfect form. He then decided to destroy the whole Earth as well as himself by self-destructing. Son Gokou was able to teleport Cell away and saved the Earth.
Who can perform it: Cell
Pl must be at 60,000. When you use this your pl increases by 17,000. You also get an extra 900 damage to your total attack damage.
Ultra Perfect Android: This form was obtained after Cell blew himself up. Since he had Saiya-jin cells in him he was able to rejenerate back to his Perfect Form. Since he doesn’t need the Androids he is considered to be Ultra Perfect. This is a major increase in pl. Gohan was the one who faught Cell in this form. Gohan started to have trouble with it but was soon able to destroy him thanx to Vegeta. That was the last time Cell was seen on Earth.
Who can perform it: Cell
Pl must be at 120,000. When you use this your pl increases by 50,000. You also get an extra 1,250 damage to your total attack damage
Nameks
Super Namek: This is the form that Piccolo took when he fused with Nail. The only things that changed was his power level, and his intelligence. Freeza was the first person to face Piccolo while he was like this. Freeza wasn’t doing so good until he transformed.
Who can perform it: Piccolo/Nail
Pl must be at 50,000. When you use this your pl increases by 21,000. You also get an extra 700 damage to your total attack damage
Super Namek 2: This form was obtained by Piccolo when he fused with Kami. Again nothing happened except for the pl increase, and his intelligence. Android 17 soon found out about this major change. The two of them were locked in battle when Cell interupted and badly beat both of them.
Who can perfom it: Piccolo/Kami
Pl must be at 110,000. When you use this your pl increases by 55,000. You also get an extra 1,300 damage to your total attack damage
Humans:
Aura 1: This isn’t really a transformation so i don’t know what it does or what happens to the person.
Who can perform it: Any human fighter
Pl must be at 20,000. When you use this you gain 3,000 pl. You also get an extra 250 damage to your total attack damage
Aura 2: Same as above.
Who can perform it: Any human fighter
Pl must be at 40,000. When you use this you gain 7,000 pl. You also get an extra 650 damage to your total attack damage
Aura 3: Same as above.
Who can perform it: Any human fighter
Pl must be at 70,000. When you use this you gain 13,000 pl. You also get an extra 850 damage to your total attack damage
Aura 4: Same as above.
Who can perform it: Any human fighter
Pl must be at 100,000. When you use this you gain 25,000 pl. You also get an extra 1,100 damage to your total attack damage
Others:
This is for any Alien not metioned above:
Transformation: This again isn’t a real transformation so i don’t know what it does or looks like.
Who can perform it: Any alien fighter
Pl must be at 25,000. When you use this you gain 4,000 pl. You also get an extra 400 damage to your total attack damage
Transformation 2: same as above
Who can perform it: Any alien fighter
Pl must be at 40,000. When you use this you gain 9,000 pl. You also get an extra 650 damage to your total attack damage
Transformation 3:same as above
Who can perform it: Any alien fighter
Pl must be at 80,000. When you use this you gain 13,000 pl. You also get an extra 900 damage to your total attack damage
Transformation 4: same as above
Who can perform it: Any alien fighter
Pl must be at 110,000. When you use this you gain 26,000pl. You also get an extra 1,200 damage to your total attack damage