Maharashtra

it will not effect on Your placement.

Yes you will be provided you get your scorecards sooner.

First of all congratulations on securing such a good scoring. You may refer the link for the Council of Architecture approved colleges.
https://www.coa.gov.in/index1.php?lang=1&level=0&linkid=25&lid=26

Yes there is NRI Quota. The fees varies from institution to institution. You can contact the respective institution for details. I would suggest you to look into the list of colleges on this link https://www.coa.gov.in/index1.php?lang=1&level=0&linkid=25&lid=26

You need to register your name for the state's competent authority, who will release a rank to you based on your NATA and 10+2 marks. Prospective applicants desirous of taking admission to First year of undergraduate course in Architecture
(Bachelor of Architecture) in India take NATA. NATA scores are used by admissions authorities of different Government, Govt. Aided & unaided schools / colleges of Architecture, to provide common measure for comparing the qualifications of applicants, for admission in addition to their scholastic performance in 10+2
or equivalent examination.

Prospective applicants desirous of taking admission to First year of undergraduate course in Architecture (Bachelor of Architecture) in India take NATA. NATA scores are used by admissions authorities of different
Government, Govt. Aided & unaided schools / colleges of Architecture, to provide common measure for comparing the qualifications of applicants, for admission in addition to their scholastic performance in 10+2 or equivalent examination.

Admission for Architecture in the state government quota's will begin around 26th June and Private management seats is already in process.