Can we migrate objects from Cognos 7 series to Cognos 10.2?

Yes, you can migrate from7 to.x.x. But it will not be a simple lift and plant process. Depending upon the current environment a upgrade/migration plan will have to be thought out.

yes, you can migrate first from 7 to 8 then to Cognos 10.2

Yes you can migrate the objects from 7.x to 10.2. But the architechture of both the environments are different. So there will be a lot of challenges during migration. In fact we did the migration from 7.4 to 10.1 in our company. Few reports might need some fix/re-creation. Documenting and using the logs at different steps will contribute in reducing the efforts during migration(we can eliminate errors or be able to understand their origin)

You can't directly migrate from Cognos 7 to Cognos 10 the process has to go through Cognos 8

Cognos 7 can be migrated but it has to migrate first in 8x then migrate to Cognos 10x

Directly cannot migrate from Cognos 7 to Cognos 10.

yes, you can move objects from ver7 to 10.x, but this will entail proper configuration of your Content Store as the ContentStores contain different structures.