Hi Natasha,

To be eligible for admission in IITs you must have qualified JEE Advanced and should have a rank under 10k if you're from general category. 

Through your JEE Main's rank, you only get admission in NITs, IIITs, and GFTIs. There are some private colleges too that accept JEE Main's rank. Below is the link for the list of all the colleges that accept JEE Main's rank:

https://engineering.careers360.com/colleges/ranking/top-engineering-colleges-in-India-accepting-jee-main-score

No,You can't apply for iits without qualifying JEE ADVANCED .It is necessary that you qualify JEE advanced and have a rank in it.You can only apply for NITs and IIITs in your option form.The JOSAA knows your profile and i think the IIT options will not be shown there.Just choose the Preferred NITs as per your interest and rank.

Hope this helps.