No, it's not wrong:
- Are you going, too? - unremarkable
- Are you going also? - slightly unsual for some speakers but fully grammatical
- Are you, too, going? - grammatical only with the commas/pauses indicated
- Are you also going? - unremarkable
I can't really explain why. The details might in principle depend on numerous factors such as person, tense, context, and whether the word too/also is potentially ambiguous in the sentence.
However, one can easily find English usage advice for the placement of also on the web - some of it even from reputable sources. One article discussing this says essentially what I just said for a first batch of example sentences. It then gives an additional example, where the earlier placement of too is more acceptable. (The author doesn't say why, but I believe it is because it starts with me as opposed to having you as the second word. There are so many instances of someone saying "Me too" and then completing this statement into a full sentence that the resulting sentences are considered unremarkable.)
No. Ook corresponds to the German word auch and the obsolete English word eke. At some point, eke got replaced by also, which (rather obviously if you think about it) originally meant completely so.
- "Dat is ook veel" = "That's also a lot" / "That's a lot as well"
- "Dat is te veel" = "That's too much"
The direct equivalent of too when it doesn't mean also / as well is Dutch te (or German zu), which is also the closest equivalent to the preposition to. That too can also be used to mean as well is a relatively late development. My language sense as a German native speaker tells me that German zu has some potential in this direction via abbreviation of dazu (thereto) and more specifically noch dazu (into the bargain, to boot), but that this potential won't be used so long as there is no reason to avoid the word auch (ook, eke). I don't know why English eke was ousted -- maybe at some point it sounded too similar to the earlier pronunciation of I? (Until the 12th century, I was spelled ic and pronounced like Dutch ik.) I guess in Dutch that would be even less likely because ertoe (thereto) doesn't seem to be used much in a similar phrase. (Nog ertoe does exist, but I don't know how popular it is.)
"Ga je ook?" is another Dutch translation of "Are you going too?"
Second person singular in Dutch is a bit funny. When the order of the personal pronoun jij/je and the verb gets reversed, the final t is lost. As Dutch words do not end in double vowels, in this case the second a is lost as well: "Je gaat ook" - "Ga je ook?"
Slightly different meaning: The Dutch sentence is about two people both going, possibly at totally different times. Go along literally means that two people are going side by side (alongside each other). Even though go along can also be used in totally abstract ways (as in going along with a proposal), when it is used in the physical sense, it always implies going together.
Sometimes it is necessary (and therefore correct) to be more specific when translating, but in this case there are perfectly good ways of saying exactly the same thing in English, therefore it's correct that go along is not accepted.