Colleges in Uttar Pradesh

Yes, definitely you can get IET Lucknow because you have a very decent rank. So, best of luck.

Yes, you can get IET, but try to sit in all rounds of counselling process specially in spot round to get IET otherwise there are strong chances for KNIT and BIET-Jhansi.

Try to use Shiksha's college predictor to know the best college according to your rank.
https://www.shiksha.com/b-tech/resources/upsee-college-predictor

Use Shiksha college predictor to know the best colleges according to your rank.
https://www.shiksha.com/b-tech/resources/upsee-college-predictor.

It's tough in IET but try to sit in all rounds of counselling, specially in spot round to get IET. Otherwise, you will have good chances of getting KNIT-Sultanpur.
I hope, it will help.

Yes you can get CSE, Electrical, mechanical branch in IET college.

Follow the link given below to get free access to Shiksha's tool which can help you in predicting the college according to your rank on the basis of previous year result:
https://www.shiksha.com/b-tech/resources/upsee-college-predictor.

In my opinion, Amity is really good for BJMC because it gives you great exposure, with the proper equipment and a great factuality to study from. For reference, you can follow the link given below to get an idea about the course and reviews from the people studying in it. https://www.shiksha.com/mas

I am sorry but I don't think Amity gives you an opportunity to do interior designing through distance learning.
However, it has Interior designing as a full-time course. For more details, please refer to the link given below:
https://www.amity.edu/course-list.aspx?fd=Interior Design&Programs=Graduate

BA history (hons) is available in Amity Noida. Follow this link to get all the required details regarding the fees, admission eligibility, etc.
https://www.shiksha.com/humanities-social-sciences/history/course/b-a-hons-in-history-amity-university-noida-232485.