Answering your questions in order
1. I want to know how is the lawyer eligible to become a judge of the court?
Lawyers can become a judge in the lower court and upwards by a combination of qualifications with exams and/or experience.
2.What are the experience requirements and educational qualifications?
A LLB degree ( 3 year or 5 year) from a recognised univeristy accepted by the BCI (Bar Council of India).
One can start a 5 year LLB course by taking the CLAT exam after 12th Standard itself.Alternatively after a graduation, one can join a 3 year course. But a 5 year course has more acceptance than a 3 year course.
To become a addition district judge one needs around 7 years of experience
To become a high court judge one needs around 10 years of experience in litigation.
The age limit to take the civil judge/magistrate exams 21-35 yrs for genearl quota.
3.Who appoints lawyer as judge?
A lawyer takes up the Qualifying exams (state Judicial services exam) to get appointed as a Civil judge (magistrates), then become Civil judge, Judicial judge and then Senior judge.
Without exams, the collegium of Judges can selection a senior advocate based on performance, experience (10 years) good standing to be appointed as Judges to high court.
From the lower courts to high court and then supreme court the promotions are based on reputation,seniority. This is more a subjective procedure of appointment.
The same collegium of Judges can appoint a SC judge by recommending a qualified high court judge to the President of India who finally authorizes the appointment of the judge in SC.
The basics favored features are honesty, integrity, reputation and litigation experience.