How can we change the shade of the crown which is permanently cemented, without removing it?

Depending on how much of it is broken and what type of crown it is, it may be possible to repair it,at least temporarily, with composite bonding. The best and longest lasting solution is to have a new crown done unless you absolutely cannot afford to. Your dentist can give you the options...

I would have  conversation with your dentist and explain why you were unable to get back in to have the crown seated and that you have paid for it and would like to work out a way to get it finished. It sounds like the dentist may not have the crown any longer, so a new impression would...

Yes, a crown can last 30 years depending on many factors including how clean you keep it, your biting habits, the type of material it was made out of, the skill of the dentist and lab,etc. If you do not take care of your crown, you can get decay at the edges of it that then can work its way up...

If the xray reveals a well done root canal, then consider that the crown is the problem.  Either a core build up around the post or a new post may be needed for better retention.  Seek another opinion but bring the xrays.

Pain after placing a crown isn't completely abnormal. There are many reasons for pain after crown placement, even if you had minimal discomfort before it was done. One cause is simply the trauma of having the tooth worked on. Another reason for pain might be that the crown is too high and is...

It is highly probable, based on what you wrote that there was gum tissue overgrowth around the temporary tooth between visits.  Your dentist, if the word trimming was used, should not confuse you with gum surgery.  It is a minor procedure.  However make sure you are satisfied with...