If we delete/change the Accounts information, will the issues that were created with the current Accounts information stay as-is, after the changes are made?

If the Account's name is changed, the new name should reflect on the issue and/or work attributes it is associated to. If an account is deleted, the information regarding that Account - in the issues and worklogs - will be removed. If you need to preserve historical data, we suggest to archive the Account instead of deleting it.