"Suddenly my credentials are no longer recognized by OpenDNS, which is actually Umbrella now, and I never logged in to it before, only to OpenDNS.com."
When you login to your dashboard at https://dashboard.opendns.com/ you should see also a link to the Umbrella dashboard (https://dashboard2.opendns.com/).
If you don't see this, then your account may not be associated with the Umbrella service. You still can use OpenDNS Home if you're a household for the purpose of blocking certain categories.
"Next, when I go through the "Forgot your password?" routine, no email gets sent to my Gmail address"
Umbrella normally does not have extra credentials unless you have configured e.g. 2-step authentication or SAML authentication. If you can login to the normal dashboard, you should be able to reach also the Umbrella dashboard, as shown above.
Not receiving the e-mail instructions indicates that Gmail handles the OpenDNS e-mail as spam. Ensure that you check the right mailbox of the e-mail address you have registered with OpenDNS. You'll have to thoroughly check your (somehow hidden) spam folder in Gmail too. You'll most likely find the OpenDNS e-mail there.
"Twitter and FB account pretend that I am not writing to them."
Not sure how Twitter and FB accounts can recognize this...
"I tried registering a new account"
In case you are already subscribed to Umbrella, this would be counterproductive, because a new account cannot come with your current Umbrella subscription. So this is not the way to go.
"the moment I specify my network, OpenDNS says that this network exists."
This is a totally different issue. It would apply to both, OpenDNS Home and Umbrella. It means that your current IP address is registered with another OpenDNS dashboard network. This can be yours (e.g. from the old account) or also another OpenDNS user's network.
If you cannot release your IP address from registration (by deleting the dashboard network) or cannot obtain another IP address by disconnecting and reconnecting your internet connection, you must raise a support ticket with OpenDNS to get your IP address released from the registration.
In your case, as you did several wrong things with e.g. creating another account, it would be best to open a support ticket with OpenDNS anyway to get you sorted unless you can solve your issues yourself after my explanations.
