Since, no one was kind enough to share their experiences, I though of elaborating the details I learnt so far one by one. I hope this will help someone in need.
(I am not an agent or an expertise in this field. details gathered only from the forums and websites. This discussion is open to add more details and share your experiences or to correct the details if any of these are false)

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CO requirements started once we submitted the application and upon the allocation of the CO for our case. Since then, CO would contact us for several reasons as verification, clarifications, for more details, corrections etc.
1. PC & HC
According to my observations, this is the first instant CO contact you. Once we lodge the application and if we did not submit the PC and HC CO will request the same from you.
PC - Police Certificate is an essential document to ensure that you are/ were in good character and you have no criminal records whatsoever. Police reports are required by the adult applicants from
all the countries where they have been residing for
last 10 years. (not required for short stays that are less than 1 year)
For Sri Lankan PC it takes 14 working days and for UK PC it takes 10 working days plus delivery period.
HC - Health Certificate or Medical Clarence are required for all the migrating and non migrating family members of your family unit.( Applicant/spouse and kids). After the lodgment of your visa application you can request for a e medical referral letter through your immi account or if you apply via an agent he or she will send the same to you (if you have not get the same from your agent, request for it). And you should visit a medical center and proceed all the required test. This takes good 4 -5 hours and the results will be submitted by the particular centre directly to authorities within a week. For Sri Lankans you can call
IOM Migration Health Assessment Centre and make an appointment.
CO will inform you if the HC is not in a good condition to proceed or if any of the test are not in satisfactory level where you might have to proceed the same process again.
Also, if you have lived in a foreign country it is a must to get the PC from that particular country as well rather than waiting for CO to remind you the same.
Conclusion - Dont wait for CO to request from you the PC and the HC as you can easily attend to those by your self. With that we can minimize the delays and CO engagements.
In my case I submitted both my UK & Local PC on the time of main application submission and my HC with in month as it was very difficult to take an appointment at the medical centre.