Design

Yes, you can, but transportation design is not available in PG in UID,its only available for UG.
But if you are interested in PRODUCT design,then Industrial Design is available in UID for PG.

You can go through the UID official website, and click on the link
https://karnavatiuniversity.edu.in/sample-paper/
You will find last year sample paper, which helps you to prepare for that examination.

Academic Fees:-
UG (B. Des.) – 2.25 Lakh per semester */ 8 semesters over 4 years = 18 Lakh for 4 Years.
To be paid in 8 installments semester wise.
There are three kinds of hostels,Twin AC, TRIPLE AC AND TRIPLE NON AC, fess varies between 1.2 to 1.7 lakh per year.

what is your qualification?

Yes, you can take admission as far as you are eligible in this.

Students who have passed Class 12th or equivalent qualifying examination can pursue the B.Des course.
Moreover, there is no restriction of stream at 10+2 level therefore; students can pursue the course irrespective of streams i.e. Science, Commerce, Arts and Humanities.
The age limit for admission to B.Des courses is minimum 19 or 20 years as specified by the institutes at the time of admission.

Yes, you are eligible to do PG course in interior & exterior design.

http://global.ctbuh.org/resources/papers/download/2003-placemaking-in-the-high-rise-city-architectural-and-urban-design-analyses.pdf
you can check resources here as well.

That's difficult to say. Many students study at unrecognised colleges for which government has no records.