My ether wallet as the name suggest is the most secure and safest wallet available on the net for which you can hold your private keys. Coming to your questions,
1. If you open an offline mew account , you got a ETH Id , is there any chance to repeat the same ID on online ? Because the offline id may not be listed in their Database.
The mew generates the private key with a random number generator. The address is a combination of 40 hexadecimal characters excluding the 0x prefix. When you are generating a address with mew offline generator, the probability of generating the same 40 character combination to be displayed again is very very low and will never happen. Firstly the private key is generated, from which a public key is derived which in turn derives the address.
A hexadecimal character is a combination of 16 characters that is (a-f) and (0-9). Hence you can generate around 16^40 possible addresses. Hence if you had picked a address, the same address will be repeated in the 16^40 address is negligible and cannot happen.
2. If you open an offline ID , then don't use it for long time. Will it get vanished ? For the above fact.
3. If it happens , what will be the correct procedure.
No way it will not at all get vanished. I can't answer to the question what can you do after the number has vanished as it will never ever happen and you can be very sure you are really secured and you will not lose your funds. Hope this answer helps.