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The additional campaign members should sync into the Genesys Cloud contact list automatically, assuming the campaign end date has not already passed. If the campaign end date has not passed, and the campaign members are still not syncing across, you want to double check that the credentials are still valid by using the "test" function in the "Shared Settings" section of the managed package. If the credentials are still ok, then you will likely need to contact customer care; they will likely ask for the log files from the campaign management section of the managed package.
Yes, that was the test function I was referring to.No, you cannot make adjustments to your campaigns in Genesys Cloud and have those sync back to Salesforce. There are a number of things that could potentially go wrong there, and that is specifically called out in the documentation as something to not do: https://help.mypurecloud.com/articles/associate-a-campaign-setting-and-a-campaign-schedule-with-a-campaign/ (see the warning at the bottom).
I would highly recommend reviewing the documentation on the campaign management feature again (https://help.mypurecloud.com/articles/about-campaign-management-genesys-cloud-salesforce/), as there are a number of helpful articles pertaining to things like proper configuration, checking logs, etc. that will help to address your questions.
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