I'll try to help you out a bit.
1. OER is used to store the artifacts and find the dependencies
2. OER is used for reuse the components ( I am struggling to understand this , because
Response: It can be. You have OER plugins you can have on your IDE and then directly make searches and reuse components. You can also use the "Download" button on OER components' pages, like a WSDL.
3. If I harvest a OSB Project , I read from blogs that artifacts will be in OER . But I would like to know if the Project is also created in OER using the same name from OSB
Response: Yes, the artifacts will be there, but in the case of harvesting from OSB, the Projects won't be created as Projects in OER.
4. Most posts tell OER design time . If its a design I see there is no point of this in production . Please clarify
Response: It is design time, because it helps you to define, structure, and evolve your artifacts throughout their whole Lifecycle, from the time they're only an idea, like a candidate service. You can use this information for your design time activities. For Runtime (and not the "production" concept you're talking about), you can use SOA Management Pack, or Oracle BTM to collect information about the services and then import that information back to OER, thus providing you additional information to take the best decisions according your needs.
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