After many hints and answers I decided to make an account since I feel like I can get some of the answers.
You can't see
But if you watch me
You might cry like a baby
and be motivated to play rugby
After googling "blind rugby" I couldn't find anything, but based on @Karun Kamal's answer, changing it to "blind rugby movie" lead to the movie Blindside.
OP added necessary to distraction, and a big explosion
I would say diversion
If I got one over my ex
Thinking along the lines of math all I have is 1/x which is indeed divergent (harmonic series) Confirming my first guess diversion
I'm always consistent
Even if you change my content
Order me around, I promise I won't byte
If the "byte" is intentional, then this must be referring to some sort of programming language? or CS in general.
This is probably hinting at a list index, if you change the contents of a list, the first element will always have 0th index... etc.
You can find me in most books
but not in some dictionaries
From that I can conclude that this is most likely index because most books have indexes but dictionaries (e.g. in python) don't have indexes, they have keys.
Add 3 to make me a gerund and add 1 to make me more
Simple and straightforward, Index $\rightarrow$ Indexing $\rightarrow$ Indexings
Ok I think I got it.
Now you have three, onto the final spree
Most probably referring to these:
Blindside, Diversion and Indexings
Get the next thrio of three
With a bit of analyzing, I noticed those 3 words above are semi-anagrams of the word inside, with an extra 3 letters.
That is blinside, diversion and indexings .
Which gave me bld, vro and xng.
What's 0 multiplied by 83?
Solved by @Mea Culpa Nay 0x83 $\rightarrow$ hex for 131
Which gives bld vro xng $\rightarrow$ box
So my answer is:
Since "box" was found in "inside", this lead me to the famous anti-phrase.
Think inside the box.
Which is definitely not what you want to do when solving the puzzle.