• There is no criteria as such for improvement exams set by the NTA (the JEE conducting body).
• So, you can give improvement exam for only those subjects for which you need to improveyour marks.

• Yes, different institutions have different admission criteria with regard to improvement exams. While some institutions take in candidates wha have sat for improvement exams, other institutions do not take in candidates who have given improvement exams.

No, you do not need to give all the subject exams. Only those in which you were not eligible due to failing or very low marks. Read the brochure of JEE Mains on the official website. You can find information regarding this. If you want to check about CBSE, then also look for its official website.