It is widely known that each Devil Fruit is unique and, as long as its user is alive, there cannot exist another with the same ability in the world.
It is quite possible that Blackbeard's body actually has multiple "beings" inside, which is why having multiple Devil Fruits doesn't kill him.
There are never two of the same Devil Fruits in the world at any time. The only exception to this are the manufactured SMILEs, but they are artificial and don't play by the same rules (and come with their own set of disadvantages, but that's for another time).
Can Luffy take second devil fruits or not? No. At present the only person who has, somehow, managed to acquire two devils fruit powers is Blackbeard, and no one knows how he did that. Normally if someone eats a second devils fruit, it'll poison them and they'll die.
The Kopi Kopi no Mi is a Paramecia-type Devil Fruit that grants the user the ability copy the abilities of other Devil Fruits.
One of the many snake Fruits seen in One Piece, the Yamata no Orochi version is considered to be the rarest out of them all. It was eaten by the Shogun of Wano, Kurozumi Orochi, and it grants him the ability to transform into an eight-headed serpent, each head having its own personality.
The Supa Supa no Mi is a Paramecia-type Devil Fruit that enables the user's body to gain characteristics of a steel blade to attack opponents with, making the user a Fullbody Bladed Human (全身刃物人間, Zenshin Hamono Ningen?, VIZ: "Human Sword"). It was eaten by Daz Bonez, also known by his Baroque Works alias Mr. 1.
Zoro can eat 3 devil fruits.
Over the years, he has come a long way and become one of the strongest pirates on the seas. Zoro has attained terrific strength, but he does not rely on a Devil Fruit at all.
All Devil Fruit eaters lose their ability to swim after consuming the Devil Fruit. It's not just a loss of muscle memory; entering a body of water saps them of all energy. Even entering a bath can drain a Devil Fruit eater of energy and prevent them from using their abilities.
The Daishou Daishou no Mi is a Paramecia type Devil Fruit eaten by Nefertari Vivi a month after the Straw Hats departed from Arabasta. It grant's the user the ability to change their size.
Devil Fruits exist in a cycle of reincarnation; when a Devil Fruit user dies, its ability is reborn into a new Devil Fruit in a random part of the world, and the one who eats it will become the new user.
Shanks is the only member confirmed to have not eaten a Devil Fruit. Shanks is the only member who is not an Admiral of a Fleet. Shanks is the only member of the original Four Emperors to not be a member of the Rocks Pirates.
It is possible that Blackbeard consumed the Inu Inu no Mi, Model: Cerberus, a Mythical Zoan-type devil fruit. Since Cerberus is known for having three heads attached to the same body, it would explain how Blackbeard managed to eat two more devil fruits, one for each head.
In the 98th volume of One Piece, Oda answered a fan question about what Devil Fruits would fit Nami, Zoro, Sanji, Usopp, and Franky best. Nami's Fruit is the Rumble Rumble Fruit, which lets its user wield the power of lightning.
In a Water 7 filler episode, Sanji finds another hint of the All Blue's existence. Salt is brought by the Aqua Laguna from all the seas and Sanji compares it to the All Blue. It is shown to be such a good seasoning that a small amount in food is enough to outclass even his own cooking.
Hito Hito no Mi, or human human fruit, is a zoan type devil fruit. This fruit's effects on humans are unnoticeable because the effect itself is turning the user into a human. If Sanji ate this fruit, the only ability he would gain is a swimming disability.
He and Jimbei are currently the only known Seven Warlords who do not have Devil Fruit powers. The only duel between Shanks and Mihawk that was actually seen is in the game One Piece: Unlimited Cruise 2.
In fact, Nami has already demonstrated abilities similar to Haki. During the Alabasta Saga, she has shown the ability to tell even the slightest of changes in weather which, according to Vivi, is beyond human comprehension.
The Sakana Sakana no Mi, Model: Shark(速いチーター Fish-Fish Fruit, Model: Shark) is a Zoan type Devil Fruit that grants the user the power to transform fully or partially into a Shark. The fruit was eaten by Zoy.
Hiya Hiya no Mi (冷冷の実 Cold Cold Fruit) is a paramecia type Devil Fruit that grants it's consumer the ability to create vast amounts of cold, making the user a Cold Human (冷の人間 Hiyano Ningen). It was eaten by Tankos Skyren.
Tetsu Tetsu no Mi is a Logia-type Devil Fruit that allows the a person to control, create, and transform into metal at will, turning the user into a Metal Human (Metaru Ningen). "Tetsu" is both the Japanese word for iron, and part of the Japanese word for steel, "koutetsu". It was eaten by Omoi Raion.
The Dark-Dark Fruit (ヤミヤミ実, Yami Yami Mi) is a Logia-type Cursed Fruit that allows the user to create, control, and transform into darkness at will, making the user a Darkness Human (闇人間, Yami Ningen).