There are two bodies who hold the IELTS examination in Sri Lanka. They are Idp Sri Lanka & British Council Sri Lanka.
There are two types of examinations
1. Paper Based Examination.
2.Computer Delivered Examination
Two to Three times for a month , but in certain months there may be 4 or 5 exams for a month.Exam is either on Thursdays or Saturdays.For exam days go to their websites.  
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Online or visiting physically you can get registered

It is Rs. 65,000 for ielts & UK visa it is Rs 74000 Go to their websites  & get the exact amount.
Paper based exam takes 13 days normally. Computer delivered exam takes around 5 days. Check with relevant bodies.
Any number of times. No restrictions for number of sittings?