When you say standard, do you mean Standard the format, also know as Type 2?
If so yes, Nicol Bolas - Planeswalker is, currently, a legal card in all formats.
The Nicol Bolas, dragon card is not legal in Standard or Extended formats.
There are two types of Nicol Bolas There's the original Nicol Bolas and then there's the Nicol Bolas Planeswalker from the Shards of Alara block.
Unless you have the first add-on pack, the Nicol Bolas expansion. The last two decks arent available to you.
Whatever someone is prepared to pay for it. For an idea, I would look at somewhere like StarCityGames (USA) or MagicMadhouse (UK) these are prices people might pay for cards, eBay completed listings will show what people are paying for cards. Which if you'd done that in the first place, you'd have an answer before you'd written your original question.
Sorin Markov is indeed a vampire who became a planeswalker. But in-game, he is never counted as a vampire spell/permanent, same as how the planeswalker forms of Nicol Bolas and Karn do not count as a Dragon/Golem.
lorwyn - ajani goldmane; jace beleren; liliana vess; chandra nalaar; garruk wildspearershards of alara - sarkhan vol; ajani vengeant; tezzeret the seeker; elspeth, knight-errantconflux - nicol bolas, planeswalkerEldrazi - sarkhan the mad, gideon jura
He Planeswalked away from Alara after Ajani beat him in a fight.
Nothing. The Planeswalker is not a Legendary Creature, and the creature is not a Planeswalker. Therefore neither the Legendary rule or the Planeswalker Uniqueness rule will come into play, even though technically you've got two cards representing the same person (this is still legally achievable in other ways too, such as both Akroma - Angel of Wrath and Angel of Vengeance)
A planeswalker is a specific card type. Like creatures, artifacts, or enchantments. It has activated abilities that add or remove loyalty counter to give you certain effects. Karn Liberated and Nicol Bolas, Planeswalker are some examples.
There are 12 known planeswalkers. Ajani Goldmane Chandra Nalaar Elspeth Tirel Garruk Wildspeaker Gideon Jura Jace Beleren Liliana Vess Nicol Bolas Nissa Revane Sarkhan Vol Sorin Markov Tezzeret the Seeker There are 16 Planeswalker cards. Ajani Goldmane Ajani Vengeant Chandra Ablaze Chandra Nalaar Elspeth, Knight-Errant Garruk Wildspeaker Gideon Jura Jace Beleren Jace, the Mind Sculptor Liliana Vess Nicol Bolas, Planeswalker Nissa Revane Sarkhan the Mad Sarkhan Vol Sorin Markov Tezzeret the Seeker
Aj Nicol's birth name is Andrew James Nicol.
Jimmie Nicol's birth name is James George Nicol.
Eric Nicol's birth name is Eric Patrick Nicol.