I have been all year 2006 under OPT. I understand I have to fill 1040NR and form 8843.
Form 8843 indicates to list the University attended and if there was any application to change status to that of a lawful permanent resident.
Do I indicate the university I graduated from even though I did not really attend school during the whole year?
Do I mention anywhere that i was under OPT?
Is the application for H1B considered an intent or an affirmative step to apply for lawful permanent resident status in the United States ?

Yes, put the university name even though you have graduated. The OPT is considered an extension of your schooling.

It is NOT necessary to say you are on OPT.

No, the H-1B is a work visa, NOT an intent or an affirmative step to apply for lawful permanent resident status in the United States.

Thanks for the great answer!

Glad to help!