Hello aspirant,

No, it is not mandatory to give B.Arch also if you want to give Btech exam only. It only gives an option that whether you want to give the entrance exam for BTech or B.Arch so that accordingly you will pursue your career with the course of your choice. But there is no compulsory to give both the exams. If you want to give Btech as well B.Arch exam, then you can go for it.

Hope, it helps you.

No , It is not mandatory to give Jee Main Paper 2. JEE MAIN Paper 2 is only required if you want to get admission in B.Arch or B.Planning. And if you wish to join only B.Tech, then Jee Main paper 1 score is required.
It is expected that the first attempt of 2021 will be conducted in February as the application has not released yet. You can start checking the official website, for any kind of updates and if the application releases it will be updated there. There might be a delay in the application of Jee Main 2021 cause most of the events of 2020 have been delayed.