The ec_eq query string parameter is the encrypted query string and is handled via the RedirectUrl.aspx process which handles the decryption of those parameters.
What's more important is that you want to carry over query parameters that are in the decrypted in the <redirectUrl>
pipeline. Because you are creating a custom Unsubscribe page that is NOT called Unsubscribe.aspx you need to specify which parameters you want to carry over in the <internalCarryoverFields>
processor of the <redirectUrl>
pipeline.
<redirectUrl>
<!--
Retrieves the message item associated with the redirect event.
-->
<processor type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.GetMessage, Sitecore.EmailCampaign.Cd" resolve="true"/>
<!--
Determines whether the link provided in the request is a reference to a page on the local web site.
-->
<processor type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CheckInternalLink, Sitecore.EmailCampaign.Cd" resolve="true"/>
<!-- Constructs the URL to redirect the request to. -->
<processor type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.SetRedirectToUrl, Sitecore.EmailCampaign.Cd" resolve="true">
<internalCarryoverFields hint="list:AddInternalCarryoverField">
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.MessageId']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.AnalyticsContactId']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.ContactIdentifierSource']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.ContactIdentifierIdentifier']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.Campaign']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.TargetLanguage']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.TestValueIndex']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
<carryoverField type="Sitecore.EmailCampaign.Cd.Pipelines.RedirectUrl.CarryoverField, Sitecore.EmailCampaign.Cd">
<param ref="settings/setting[@name='QueryStringKey.EmailHistoryEntryId']/@value" desc="fieldKey"/>
<param desc="urlPattern">
SubscriptionPreferences.ashx|.*ConfirmSubscription.aspx|.*Unsubscribe.aspx|UnsubscribeFromAll.aspx.*|.*sc_pd_view=1.*
</param>
</carryoverField>
</internalCarryoverFields>
</processor>
Adding your Newsletter.aspx page to the urlPattern parameters will allow the fields you are looking for in your Newsletter.aspx page to be available.