Here is the paper I am reading "Guide to the Serre Spectral Sequence in 10 easy steps!"(it is found free online but I do not know how to attach it):
The paper said that "going out of row 1 and 2 of the $E_3$ page all the differentials are zeros" but I am not sure why this is correct, what should be the length of the differential arrow in the $E_3$ page, could someone explain this to me please?
I'm assuming you're talking about the sentence on p. 2.
On p. 1 of the document, the author says, $d_r: E_r^{s,t} \to E_r^{s+r,t-r+1}$. That is, $d_r$ goes to the right by $r$, down by $r-1$. At $E_3$, for example, the differentials go down by 2, and since there is nothing below row 0, there are no possible nonzero differential starting in rows 0 and 1. This is indicated in the picture. The text also says that the differentials starting in row 2 must be zero, but this is wrong and it is also contradicted by their own picture. Indeed, the picture on p. 8 (and the ensuing computation) shows a nonzero $d_3$ starting in row 2. Including row 2 in the sentence on p. 2 is a mistake.