From while and when, which will you prefer and why? If it is possible, please say another word that can used instead of while and when in this case.
In the temporal sense,
"While" deals with a duration,
While I was sleeping, he stole my phone.
"when" deals with some specific point in time.
When I went to bed, he stole my phone.
In your case, I prefer
Every single day when I sit to write, I am to think what I will write.
I would use your option 2:
Every single day when I sit to write, I should start with thinking about what exactly I will write.
The second option focuses too much on the process of sitting:
Every single day while I sit to write, I am to think what I will write.
It's hard for me to construe a situation where this sentence would be felicitous. Maybe you have two chairs. On the first chair, you "sit to write": the chair is used solely for sitting and thinking about what exactly to write. The second chair is used when you've finally decided what it is that you should write.
There are subtle differences between the meaning of the two sentences.
"While I sit to write"
refers to the entire period of time spent sitting.
"When I sit to write"
refers to the action of sitting down; i.e. one specific moment.
