[SalesForce] Marketing Cloud Connector problem

It will impact more or less everything that relies on Sales Cloud data, so all the points you listed will be affected plus some additional functions like Tracking Data, cross-cloud AMPScript and so on.

There is a short documentation article available on Disconnecting the Clouds and what happens when you do so.

In short, yes, you will need to configure your Synchronised Data Extensions again and map the fields.

Journeys will be impacted if they are either based on Salesforce Entry Data, have Sales Cloud events or you have some Split Decisions configured using the Sales Cloud Data, or your Emails/SMS use cross-cloud AMPscript.

Though as mentioned before, the tracking activity will be stopped entirely for the downtime and there is no way to get the 'lost' IER's later created in Sales Cloud.

I've seen this error a bunch of times and the only solution that has worked 100% of the time is to delete the package and reinstall. But you should follow these steps below before deleting and reinstalling the managed package (it helps to use an incognito window of Chrome as you may have other instances of CRM or MC open):

1. You mentioned that you checked the permissions. Double check that the authentication settings are correct in CRM. And double check that you have applied admin permissions.
2. Check the Permission Sets are assigned correctly to the correct user
3. Also in CRM, you should be able to click the Connect to Marketing Cloud blue button.
4. Theoretically, the Setup Wizard should create the connection and add the whitelist IP addresses automatically.
5. If you're unable to get into the configuration settings, use this URL hack and add "apex/marketingcloudconfiguration" at the end of your URL. i.e. https://etxxxx.xxxx.visual.force.com/apex/marketingcloudconfiguration.
6. Refer to the image above: Under Manage Business Units, make sure you have the business unit checked
7. Under Manage Users, make sure you have your MC user checked for both User and Admin.
8. In Marketing Cloud > Setup > Users, click the "Integrate" link and add your CRM login and save it so it shows Integrated.

8. Back in CRM, in the Marketing Cloud Connector Settings, check that the API User Username matches your MC User. If not, then click the Change API User link.

9. If all else fails, delete the managed package and re-install the managed package.

I would make sure you try all the steps above before deleted and re-installing (I have a feeling it could be #2 above). But since you are on multi-org, I assume that this managed package is a fresh install in the org and it should not be an issue to delete the package and reinstall it.