Chayan Patra

In the real "Physical World", which is perceptible to us, we have just three dimensions. Nothing else! 

There are notions of higher dimensions, but they are not Physically understandable spaces! For example, Phase Space is multidimensional. We use Hilbert Space in Quantum Mechanics which is infinite-dimensional! But these are not real physical spaces. They are abstract spaces to describe a system and for calculational conveniences! Special Relativity is carried out in an area called Minkowski Space which is 4 Dimensional, and the fourth dimension is time itself! But the geometry changes there. It's different from the Geometry you've studied till now (known as Euclidean Geometry). 

You can search Minkowski space, Phase Space, Hilbert Space on Google, if interested! 

No, Newton's Second Law and First Law are independent laws! The first law gives us the notion of an inertial frame, in which the second law is valid! A lot of school-books have this section "Derivation of 1st law from 2nd law", but this is absurd. If you read books like Kleppner-Kolenkow, Berkeley Physics or Feynman Lectures, you'll get to know that the three laws are entirely independent and maintain a proper sequence.

The first law tells us about the inertial frame of reference, in which we can use F=ma. If the frame is not inertial, we have to take the Pseudo Forces into account which is non-Newtonian! Whenever we write F=ma, we inherently assume the first law. So there's no point to prove 1st law from the 2nd! 

To give an analogy - asking to prove 2nd law from the 1st law is like asking someone to prove that he/she was born because he/she has parents! I think I can make my points clear! 

So, don't ever have this concept that these two laws are dependent, and they are not individual cases of one another! They're entirely independent! Don't believe those class 9-10 Physics books. Have a look at my references if interested! You'll get to know how beautiful and profound Newton's three laws are!